The correct answer is C. A new substance forms when the batter is cooked.
Explanation:
When a chemical change occurs the properties, and composition of substances change. This means atoms in the substance re-arrange to form a new substance. This only occurs when there is a chemical change, but not when physical changes occur, indeed a physical change only affects the state of the matter, shape, size, etc.
In the case of the pancake, this is an example of a chemical change because though the process of cooking the pancake changes its composition. Due to this, the properties of the cooked pancake, and the butter are not the same as a new substance forms. Also, in this and most chemical changes, reversibility is not possible, that is why you cannot reverse the process and make the cooked pancake batter once again.
Answer:
C. on edge
Explanation:
Charlene has just begun to be able to form a mental representation of an object that is not visibly
present According to Piaget, that means that she has made the transition from the
stage
to the
stage
According to Piaget, that means that she has made the transition from the sensorimotor to preoperational stage
What is the sensorimotor stage?The first of Piaget's four stages of cognitive development is the sensorimotor stage.
A child's understanding that the outside world exists apart from them is what distinguishes it.
Within Piaget's stages of development, the kid will advance to the following stage after they have completely grasped this.
"Charlene has just begun to be able to form a mental representation of an object that is not visibly present.
According to Piaget, that means that she has made the transition from the sensorimotor to preoperational stage
Only recently has Charlene been able to create a mental image of something that is not physically present.
That indicates that she has moved from the sensorimotor to the preoperational level, in accordance with Piaget.
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If you blow harder into a trumpet you will create a sound wave with a greater
A. pitch
B. amplitude
C wavelength
Answer is C
Explanation:
Answer:
C. wavelength
good luck, i hope this helps :)
A glass optical fiber is used to transport a light ray across a long distance. The fiber has an index of refraction of 1.520 and is submerged in ethyl alcohol, which has an index of refraction of 1.361. What is the critical angle (in degrees) for the light ray to remain inside the fiber
Answer:
θ = 63.5º
Explanation:
When a ray of light strikes the separation surface between two transparent media with different index of refraction, part of the light remains in the first medium, and part transmits to the second one , according to the Snell's Law, as follows:\(sin \theta_{i}* n_{i} = sin \theta_{r}* n_{r} (1)\)
where θi = angle of incidence (with the normal to the surface)
θr = angle of refraction (with the normal to the surface)
ni = index of refraction of denser medium = 1.520
nr = index of refraction of less dense medium = 1.361
When the angle of refraction is equal to a right angle, this means that the light is parallel to the surface, and remains within the first medium completely.The angle of incidence for this particular angle, is called the limit angle, and is the principle of operation of fiber optics, which are composed by a strand of glass, surrounded with another material, which index of refraction is lower than the fiber's, preventing light to go outside the fiber.In our case, replacing ni, nr, and θr = 90º in (1), we get:\(sin \theta_{i}* 1.520 = 1* 1.361 (2)\)Solving for sin θ₁ :\(sin \theta_{i} = \frac{1.361}{1.520} = 0.895 (3)\)
⇒ θi = sin⁻¹ (0.895) = 63.5º
A sphere or cylinder of mass M, radius R, and moment of inertia I rolls without slipping down a hill of height h, starting from rest. If there is no slipping w = Vcm/R.(a) In terms of the given variables (M , R , I , and h ), what is vCM at the bottom of the hill? (Use any variable or symbol stated above along with the following as necessary: g for the acceleration due to gravity.)
vCM at the bottom of the hill is \(\sqrt{2Mgh}\) / \(\sqrt{M+(1/R^{2}) }\). One of the most famous physics rules is the law of conservation of momentum. The overall momentum of a system is always conserved for an isolated system, according to the conservation of momentum law principle.
By the law of conservation of momentum
E₁ = E₂
U₁ + K₁ = U₁ + K₁
U₁ + \(K_{t}\) = \(u_{f}\) + \(K_{uf}\) +k
The object is initially at rest hence the initial kinetic energy is zero. Finally, the object is at the bottom of the hill. That is the height is zero. Hence the final potential energy is zero.
Mgh = 1/2 MV² + 1/2 1ω²
Velocity is
Mgh = ( 1/2MV² + 1/2 l [v²/R])
Mgh = \(\sqrt{2Mgh\frac}\) /\(\sqrt{M+(1/R^{2} } )}\)
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what did you notice about the total momentum before the collision and the total momentum after the collision in each of the above cases
There is a difference in total momentum before collision (3.212) and total momentum after collision (32.007).
The total momentum before and after a collision is conserved in an isolated system, meaning that the total momentum of the objects before the collision is equal to the total momentum of the objects after the collision. This is known as the law of conservation of momentum.
The law of conservation of momentum is a fundamental concept in physics that states that the total momentum of a closed system remains constant, unless acted upon by an external force. This law states that the momentum of an isolated system remains constant, regardless of any internal or external forces. The law of conservation of momentum is a consequence of the law of energy conservation and is a fundamental principle in mechanics, and it applies to both linear and rotational motion.
The law of conservation of momentum can be applied to a wide range of physical systems, including collisions between objects, explosions, and the motion of objects in space. In the case of a collision between two objects, the total momentum of the objects before the collision is equal to the total momentum of the objects after the collision, provided there is no external force acting on the system. This law is used to predict the velocity and direction of objects after a collision, as well as the amount of energy transferred during the collision.
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Complete Question: -
What did you notice about the total momentum before the collision and the total momentum after the collision in each of the above cases?
The principle you should have noted in the previous question is called conservation of momentum. What do you think it means to say something is conserved in the context of physics?
Why losing is an important aspects of sports
Answer:
It reminds us that we need to work harder. It allows us to make adjustments in the way and manner in which we train and practice. In a loss, we are able to identify our vulnerabilities and weaknesses, and work to improve.
Explanation:
what is the physics behind why electric parallel plates move from positive to negative
The physics behind the movement of electric charges between parallel plates is based on the principles of electrostatics. Electric charges are either positive or negative, and they are affected by electric fields.
Electric fields are created by a difference in electric potential, which is measured in volts. When a voltage is applied to a set of parallel plates, the charges within the plates will be affected by the electric field, and will move in response to it.
What are electric parallel plates?When a voltage is applied to a set of parallel plates, the positive charges in the plate connected to the positive voltage will be attracted to the negative voltage, while the negative charges in the plate connected to the negative voltage will be attracted to the positive voltage.
The movement of charges between the plates is also affected by the presence of any obstacles or resistances in the electric field, such as resistance in the wire. This can slow down the movement of charges and result in a decrease in the current flowing through the circuit.
In all, the movement of charges between electric parallel plates is the result of the electric field created by a difference in electric potential, and the movement of charges is called drift velocity. The movement is also affected by the presence of resistance.
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An aeroplaneflying above groundnd490m with 100 meterpersecond how far on ground it will strike
The airplane will strike the ground at a horizontal distance of 490 meters.
To determine how far the airplane will strike on the ground, we need to consider the horizontal distance traveled by the airplane during its flight.
The horizontal distance traveled by an object can be calculated using the formula:
Distance = Speed × Time
In this case, the speed of the airplane is given as 100 meters per second and the time it takes to cover the distance of 490 meters is unknown. Let's denote the time as t.
Distance = 100 m/s × t
Now, to find the value of time, we can rearrange the equation as follows:
t = Distance / Speed
t = 490 m / 100 m/s
t = 4.9 seconds
Therefore, it takes the airplane 4.9 seconds to cover a horizontal distance of 490 meters.
Now, to calculate the distance on the ground where the airplane will strike, we can use the formula:
Distance = Speed × Time
Distance = 100 m/s × 4.9 s
Distance = 490 meters
It's important to note that this calculation assumes a constant speed and a straight flight path. In reality, various factors such as wind conditions, changes in speed, and maneuvering can affect the actual distance traveled by the airplane.
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The cost of gas is $1.27 per liter. How much does a gallon of gas costs?
The cost of gas is $1.27 per liter and the gallon of gas costs $4.80. where 1 gallon is equal to 3.78541 liters.
To convert the cost of gas from dollars per liter to dollars per gallon, The conversion factor between liters and gallons.
1 gallon is equal to 3.78541 liters (the exact conversion factor is 3.785411784).
Given the cost of gas is $1.27 per liter, let's calculate the cost per gallon:
Cost per gallon = Cost per liter × Liters per gallon
Cost per gallon = $1.27 × 3.78541
Cost per gallon = $4.80
So, a gallon of gas costs $4.80.
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How long does it take light from a camera to travel to the face of someone standing 7 meters away?
The time taken for the light to travel from the camera to someone standing 7 m away is 2.33×10¯⁸ s
Speed is simply defined as the distance travelled per unit time. Mathematically, it is expressed as:
Speed = distance / timeWith the above formula, we can obtain the time taken for the light to travel from the camera to someone standing 7 m away. This can be obtained as follow:
Distance = 7 m
Speed of light = 3×10⁸ m/s
Time =?Time = Distance / speed
Time = 7 / 3×10⁸
Time = 2.33×10¯⁸ sTherefore, the time taken for the light to travel from the camera to someone standing 7 m away is 2.33×10¯⁸ s
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Water in a metal pot is heated over a campfire. Primarily, by wat means of energy transfer is thermal energy moved from the fire to the bottom of the pot?
when water in a metal pot is heated over a campfire. Primarily, by means of convection energy transfer is thermal energy moved from the fire to the bottom of the pot
What is thermal energy?It can be defined as the form of the energy in which heat is transferred from one body to another body due to their molecular movements, thermal energy is also known as heat energy.
Thermal energy can flow by different means such as conduction, convection, and radiation.
As given in the problem when water in a metal pot is heated over a campfire. The energy we receive around the campfire is mostly due to the effect of the radiation of the heat but the Primary means of energy transfer is thermal energy moved from the fire to the bottom of the pot because of the convection.
Thus, when water is heated in a metal pot over a campfire. Thermal energy is primarily transferred from the fire to the bottom of the pot through convection.
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A positively charged solid nonconducting cylinder of length ℓ = 10 m and radius R = 50 mm has uniform volume charge density + 7.0 × 10−9 C/m3. What is the charge inside the cylinder?
The charge inside the cylinder is 15.81 N/C.
length ℓ = 10 m
radius R = 50 mm = 50 x 10^-3 m
volume charge density ρ = + 7.0 × 10^−9 C/m3.
the charge inside the cylinder Q = ρV
Where V = Volume of the cylinder
= πR^2 l
= 3.1415 x (50x10^-3)^2(10)
= 78.53 x10 -3 m^3
Therefore Q = (+ 7.0 × 10^−9 C/m^3)( 78.53 x10^-3 m^3)
= 5.4971 x10^-10 C
The electric field magnitude at r = 40 mm, where r is the radial distance from the long central axis of the cylinder
E = ρr/ε _{o}
Where ε _{o} = permitivity of free space = 8.85 x10^-12 C^2/Nm^2
r = 40 mm = 40 x10^-3 m
Substitute values you get ,
E = (7 x10^-9 )(40x10^-3 ) /[2 x8.85 x10^-12 ]
= 15.81 N/C
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Explain what causes seasons. What is the difference between winter solstice and summer solstice?
Answer: The axial tilt of the Earth
Explanation: The planet is tilted on its north-south axis by 23 degrees, making one hemisphere (out of northern and southern) closer to the sun than the other for half of the year. The hemisphere that's closer to the earth at any point experiences summer, and the one further away experiences winter.
Answer: The difference between the solstices is that one represents the point at which the hemisphere in question is closest to the sun (summer solstice) and furthest away (winter solstice)
e=mc² what is the name of the law?
Answer:
The name of law is mass engery law
Which of the following would you expect to be a strong electrolyte in solution?
The following would expect to be a strong electrolyte in solution (b) KCI is correct option.
When dissolved in water, a strong electrolyte produces a large concentration of ions in solution by totally dissociating into ions. The following compounds are typically strong electrolytes in solution according to this definition:
Al(OH)₃ (aluminum hydroxide) is a weak electrolyte. It does not dissociate significantly into ions in solution, resulting in a low electrical conductivity.KCl (potassium chloride) is a strong electrolyte. It completely dissociates into potassium ions (K⁺) and chloride ions (Cl⁻) in solution, resulting in a high concentration of ions and a high electrical conductivity.PbI₂ (lead(II) iodide) is a weak electrolyte. It does not dissociate significantly into ions in solution, resulting in a low electrical conductivity.These substances readily dissociate into ions in water and exhibit high electrical conductivity, making them strong electrolytes in solution.
Therefore, the correct option is (b).
The complete question is,
Which of the following would be a strong electrolyte in solution?
a) Al(OH)₃ b) KCI c) Pbl₂
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A 50gram bracelet is suspected of not being pure gold. It is dropped into a glass of water and 4 cm3of water overflows. Is the bracelet pure gold? How do you know?
Since, density of the bracelet is not equal to the density of gold, then, the bracelet is not pure gold.
To know if the bracelet is pure gold, we calculate the density of the bracelet and compare it to the density of pure gold (19.3 g/cm³).
That is, for the bracelet to pure gold,
Density of bracelet ≈ 19.3 g/cm³
What is Density?Density can be defined as the ratio of the mass and the volume of a substance.
The formula of Density is give as
D = m/v................... Equation 1⇒ Where:
D = Density of the braceletm = mass of the braceletv = volume of the braceletFrom the question,
⇒ Given:
m = 50 gv = 4 cm³ (an object displace an amount of water equal to it's own volume)⇒ Substitute these values into equation 1
D = 50/4D = 12.5 g/cm³Hence, since the density of the bracelet is not equal to the density of gold, then, the bracelet is not pure gold.
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1. The kinetic energy of a car is 8 106 J as it travels along a horizontal road. How much work is required to stop the car in 10 s? (A) zero joules (B) 8 105 J (C) 8 107 J (D)8 104 J (E) 8 106 J
The power to stop the car with kinetic energy of a car is \(8*10^{6} J\) as it travels along a horizontal road is \(8*10^{5} watt\), option B
What is Kinetic energy ?Kinetic energy can be seen as one that is been recorded when an object is able to move from a place , in a broad term we can say this is the energy that can be attributed to that of someone leaving a place and go to another place hence we can see it as the one in the motion.
The definition of energy as the "power to accomplish work" refers to the capacity to apply a force that moves an object. Even if the word is vague, it is clear what energy actually means: it is the force that causes objects to move. The two types can be attributed to the one we know which are kinetic and potential energy.
\(Power \frac{Energy}{time}\)
\(Energy = 8*10^{6} J\)
\(time = 10 s\)
\(Power = \frac{8*10^{6} J}{10}\)
\(power = 8*10^{5} watt\)
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proper question;
The kinetic energy of a car is 8 × 106 J as it travels along a horizontal road. How much power is required to stop the car in 10 s? (A) zero joules (B) 8 105 J (C) 8 107 J (D)8 104 J (E) 8 106 J
If the acceleration of the body is towards the center, what is the direction of the unbalanced force ? Using a complete sentence , describe the direction of the net force that causes the body to travel in a circle at a constant speed.
Accelerating objects are changing their velocity. Velocity is often thought of as an object's speed with a direction. Thus, objects which are accelerating are either changing their speed or changing their direction. They are either speeding up, slowing down or changing directions. Changing the velocity in any one of these three ways would be an example of an accelerated motion.
The half-life of cesium-137 is 30 years. Suppose that we start with 60 grams of cesium-137 in a storage pool.
How many half-lives will it take for there to be 10 grams of cesium-137 in the storage pool? (Round answer to two decimal places.)
How many years is that? (Round answer to one decimal place.)
9514 1404 393
Answer:
2.58 half-lives77.5 yearsExplanation:
The remaining amount, in terms of t half-lives, is ...
q(t) = 60·(1/2)^t
We want t when q(t) = 10, so ...
10 = 60·(1/2)^t
1/6 = (1/2)^t . . . . . . divide by 60
log(1/6) = t·log(1/2) . . . . take logs
t = log(1/6)/log(1/2) = -0.778151/-0.30103 ≈ 2.58496
It will take about 2.58 half-lives for there to be 10 grams remaining.
In years, that is 2.58×30 = 77.5 years.
Part-II Work out Step by step clearly (6%) 5. A 5kg mass starts from rest at xo = -1 and moves under the action of a variable force F(x) = √1-x² to point xf = 1. Calculate the total work done by the force? (1%)
If a 5kg mass starts from rest at xo = -1 and moves under the action of a variable force F(x) = √1-x² to point xf = 1. Then the total work done by the force is equal to π/2 + 1.
To calculate the total work done by the force in this scenario, we can use the formula for work:
Work = ∫F(x) dx
where F(x) is the force as a function of position and dx represents an infinitesimal displacement.
In this case, the force is given by F(x) = √(1 - x²), and we need to find the total work done as the object moves from xo = -1 to xf = 1.
Let's break down the calculation step by step:
Write the integral for work:
Work = ∫F(x) dx
Substitute the given force:
Work = ∫√(1 - x²) dx
Integrate with respect to x:
To integrate the square root of (1 - x²), we use the trigonometric substitution. Let's substitute x = sin(θ) and dx = cos(θ) dθ.
Work = ∫√(1 - sin²(θ)) cos(θ) dθ
Simplify the integrand:
Using the trigonometric identity sin²(θ) + cos²(θ) = 1, we can rewrite the integrand as cos²(θ).
Work = ∫cos²(θ) dθ
Apply the power-reducing formula:
The power-reducing formula states that cos²(θ) = (1 + cos(2θ)) / 2. We can use this formula to simplify the integrand further.
Work = ∫(1 + cos(2θ))/2 dθ
Integrate the terms separately:
Work = (1/2) ∫dθ + (1/2) ∫cos(2θ) dθ
The first integral, ∫dθ, is simply θ, and the second integral, ∫cos(2θ) dθ, can be calculated as sin(2θ)/2.
Work = (1/2) θ + (1/2) (sin(2θ)/2) + C
Evaluate the integral limits:
To find the total work done, we need to evaluate the integral at the upper and lower limits of integration.
At xf = 1, the angle θ is π/2, and at xo = -1, the angle θ is -π/2.
Work = (1/2) (π/2) + (1/2) (sin(2(π/2))/2) - [(1/2) (-π/2) + (1/2) (sin(2(-π/2))/2)]
Simplifying further:
Work = π/4 + (1/2) - (-π/4 + (1/2))
Work = π/4 + 1/2 + π/4 + 1/2
Work = π/2 + 1
Therefore, the total work done by the force is equal to π/2 + 1.
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5.33 A constant force F= (4.70-379, 2.09) N. acts on an object of mass 180 kg, causing a displacement of that object by F= (4.25, 3.69-245) m What is the total work done by this force
The total work done by this force is 28.9-1457.86 N m.
What is total work?Total work is the sum of all the energy expended in completing a job or task. It is the amount of effort and energy expended to accomplish a goal or complete a task. Total work can be calculated by adding up all of the individual components of the job or task, such as time, effort, and materials.
The total work done by this force can be calculated using the formula W = F * Δx, where F is the force vector, and Δx is the displacement vector. In this case, the total work done is:
W = (4.70-379, 2.09) * (4.25, 3.69-245) = (19.9-944.81, 8.00-513.05) N m
Therefore, the total work done is 28.9-1457.86 N m.
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a current of a 6 flows through a light bulb for 12 s, how many coulombs of charge pass through the light bulb during this time
A current of a 6 flows through a light bulb for 12 s. The total charge that passes through the light bulb during the given time is 72 coulombs.
To calculate the total charge that passes through the light bulb, we need to use the formula Q = I * t, where Q represents the charge in coulombs, I represents the current in amperes, and t represents the time in seconds.
Step 1: Identify the known values:
Current (I) = 6 amperes
Time (t) = 12 seconds
Step 2: Calculate the charge using the formula:
Q = I * t
Step 3: Substitute the known values into the formula:
Q = 6 amperes * 12 seconds
Q = 72 coulombs
Therefore, the total charge that passes through the light bulb during the given time is 72 coulombs.
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HELP PLZZZZZ
Vitiligo is an example of a condition that comes from
A. your habits
B. your predisposed genetics
C. your social network
D. your physical environment
Answer:
the answer is b vitiligo is a genetic skin condition
can anyone write for me all the equation of linear motion
All the equations of motion are as follows, Displacement (s) equation, Final velocity (v) equation, Average velocity (v_avg) equation, Displacement (s) equation with average velocity, and Displacement (s) equation.
Equations of MotionIn terms of its motion as a function of time, equations of motion define how a physical system behaves. In more detail, the equations of motion define how a physical system behaves as a collection of mathematical functions expressed in terms of dynamic variables.
s = ut + (1/2)at^2v = u + atv_avg = (u + v) / 2s = v_avg * ts = (u + v) / 2 * tv^2 = u^2 + 2asIn conclusion, equations of motion define how a physical system behaves in terms of how its motion changes over time.
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What is the symbol F g mean
Answer:
Disambiguation
Explanation:
Fg is an abbreviation used in physics to describe the amount of force exerted by gravity on an object, normally represented in units such as the newton.
Answer:Gravitational forces
Explanation:Is used in physics, used when asked to calculate the the force attracted to the nucleus
In the given figure a 0.250 kg block of cheese lies on the floor of a 900 kg elevator cab that is being pulled upward by a cable through distance d1=2.40 m and then through distance d2=10.5 m. (a) Through d1, if the normal force on the block from the floor has constant magnitude FN=3.00 N, how much work is done on the cab by the force from the cable?
(b) Through d2, if the work done on the cab by the (constant) force from the cable is 92.61 kJ, what is the magnitude of FN?
In the given figure a 0.250 kg block of cheese lies on the floor of a 900 kg elevator cab that is being pulled upward by a cable through a distance d₁=2.40 m and then through a distance d₂=10.5 m.
The work done on the cab is also zero. the magnitude of Fₙ is F= 7.179 kN.What is the work done?Generally, To find the work done on the cab by the force from the cable in part (a), we can use the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy.
Since the cab is not accelerating, the change in its kinetic energy is zero, and so the work done on the cab is also zero.
In part (b), The work done on the cab by the cable is given as 92.61 kJ. The change in kinetic energy of the cab is equal to its final kinetic energy minus its initial kinetic energy. Since the initial kinetic energy of the cab is zero (it starts at rest), the change in kinetic energy of the cab is equal to its final kinetic energy.
The final kinetic energy of the cab can be expressed as:
KE = (1/2) * m * v^2
Where KE is the kinetic energy, m is the mass of the object, and v is the velocity of the object.
Since we are given that the mass of the cab is 900 kg and we are trying to find the velocity of the cab, we can rearrange the equation to solve for v:
v = √(2 * KE / m)
Substituting the values for KE and m, we get:
v = √(2 * 92.61 kJ / 900 kg)
v= 0.45365m/s
Now that we know the velocity of the cab, we can use the work-energy principle to find the force exerted on the cab by the cable.
The work done on the cab by the cable is given as 92.61 kJ, and the distance the cab moves is given as
d1 + d2 = 2.4 m + 10.5 m
= 12.9 m.
The force exerted on the cab by the cable is given by the equation:
F = W / d
Substituting the values for W and d, we get:
F = 92.61 kJ / 12.9 m
F= 7.179 kN
Therefore, the magnitude of Fₙ is 7.21 kN.
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Complete Question not found
Figure not found
Two piloted satellites approach one another at a relative speed of 0.25 m/s, intending to dock. The
first has a mass of 4.00 × 103 kg, and the second a mass of 7.50 × 103 kg. If the two satellites collide
elastically rather than dock, what is their final relative velocity?
Jane (m=50kg) wants to save Tarzan (m= 80kg) who is standing in the middle of a ring of fire of 5.0 m diameter. Jane has a vine (conveniently attached to a branch right above Tarzan, at a height of 33 m above the ground. Jane holds onto the vine and climbs a tree, growing 16 m away from Tarzan, until she reaches a height of 5.3 m above the ground. She swings down and grabs Tarzan around his waist (1.0m above ground). If they let go of the vine when they reach their highest point, where will they land, relative to Tarzan's original position?
The height that will illustrate the distance will be d = 6.36m
How to calculate the height?Based on the information given, the length of the vine will be:
L = ✓(16² + 27.7)²
L = 32m
The velocity of Jane when she reaches position B will be:
V = ✓2gh
V = ✓(2 × 9.8 × 4.3)
V = 9.18m/s
We will apply the conversation of momentum. This will be:
50 × 9.18 = (50 + 80)V1
V1 = 3.53m/s
Therefore, the height that will illustrate the distance will be:
31.36² + d² = 32²
d² = 32² - 31.36²
d = 6.36m
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5. You are concentrating on an exam, deciding between two answers that could possibility be right
for one of the questions. What part of the brain is activated during this task?
a. Temporal lobe
b. Occipital lobe
C.
Parietal lobe
d. Prefrontal cortex
Answer: D. prefrontal cortex
Explanation: The Prefrontal Cortex (PFC) and hippocampus are the most critical parts of the human brain for decision making
Gretchen runs the first 4.0 km of a race at 5.0 m/s. Then a stiff wind comes up, so she runs the last 1.0 km at only 4.0 m/s.
If she runs fhe same course again, what constant speed would let her finish in the same time as in the first race?
Answer:
The velocity is \(v = 4.76 \ m/s\)
Explanation:
From the question we are told that
The first distance is \(d_1 = 4.0 \ km = 4000 \ m\)
The first speed is \(v_1 = 5.0 \ m/s\)
The second distance is \(d_2 = 1.0 \ km = 1000 \ m\)
The second speed is \(v_2 = 4.0 \ m/s\)
Generally the time taken for first distance is
\(t_1 = \frac{d_1 }{v_1 }\)
\(t_1 = \frac{4000}{5}\)
\(t_1 = 800 \ s\)
The time taken for second distance is
\(t_1 = \frac{d_2 }{v_2 }\)
\(t_1 = \frac{1000}{4}\)
\(t_1 = 250 \ s\)
The total time is mathematically represented as
\(t = t_1 + t_2\)
=> \(t = 800 + 250\)
=> \(t = 1050 \ s\)
Generally the constant velocity that would let her finish at the same time is mathematically represented as
\(v = \frac{d_1 + d_2}{t }\)
=> \(v = \frac{4000 + 1000}{1050 }\)
=> \(v = 4.76 \ m/s\)
The constant speed that will let her finish in the same time as in the first race is 4.76 m/s
Determination of the time taken for first 4 KmDistance = 4 Km = 4 × 1000 = 4000 mSpeed = 5 m/sTime 1 =?
Time 1 = distance / speed
Time 1 = 4000 / 5
Time 1 = 800 s
Determination of the time taken for the last 1 KmDistance = 1 Km = 1 × 1000 = 1000 mSpeed = 4 m/sTime 2 =?Time 2 = distance / speed
Time 2 = 1000 / 4
Time 2 = 250 s
Determination of the constant speedTotal distance = 4000 + 1000 = 5000 mTotal time = 800 + 250 = 1050 sConstant speed =?Constant speed = Total distance / total time
Constant speed = 5000 / 1050
Constant speed = 4.76 m/s
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