Question 12 (10 points)
4) Listen
Ď (10,0 m)
25.00
Answer
53.0
B (15.0 m)
30,00
X
č (12.0 m)
X (8.00m)
For the vectors shown in the figure above
A+B+B. What is the
magnitude of
Note: Your answer is assumed to be reduced to the highest power possible.
Your Answer:
x10
units

The point where the driver stops the car is 3/4 of the way around the track in the counter-clockwise direction.

a. The circumference of a circle is given by the formula 2πr, where r is the radius.

So, if the radius is 6 kilometers, the circumference is 2π(6) = 37.7 kilometers.

b. The point where the driver stops the car is 3/4 of the way around the track in the counter-clockwise direction.

In Cartesian coordinates, this corresponds to the point (-r, -r), where r is the radius. So, the coordinates are (-6, -6) to the nearest whole number. In terms of tenths, that's (-6.0, -6.0).

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The Complete Question

In Italy, there is a large circular test track that is used to test race cars and other high-speed automobiles. a. Suppose a similar track has a radius of 6 kilometers. Find the circumference of the track b. While test-driving a new car on the similar track, a driver starts at the right-hand side of the circular track, travels in a counter-clockwise direction, and stops of the way around the track. Using the center of the track as the origin and the starting point as the intersection of the x- axis and the circle represented by the track, find the coordinates, to the nearest tenth, of the point where the driver stopped the car.

Answer:

To find the height at which the two objects will first meet, we need to use the equations of motion for free fall and vertical upward motion.

The equation for free fall is:

h = h0 + v0t + (1/2)at^2

where h is the height of the object at time t, h0 is the initial height, v0 is the initial velocity (which is zero for free fall), and a is the acceleration due to gravity (which is 9.8 m/s^2 downward).

The equation for vertical upward motion is:

h = h0 + v0t - (1/2)gt^2

where h is the height of the object at time t, h0 is the initial height, v0 is the initial velocity, and g is the acceleration due to gravity (which is 9.8 m/s^2 downward).

We know that the first object is in free fall, and that it began at a height of 22.0 m. We also know that the second object was launched upward with an initial velocity of 32.0 m/s, 1.10 s after the first object was released.

We can use these values to find the height of the first object at the time the second object is launched:

h1 = 22.0 + 0 + (1/2)(-9.8)(1.10^2) = 20.27 m

We can use this value as the initial height for the second object:

h2 = 20.27 + 32.0(1.10) - (1/2)(-9.8)(1.10^2) = 37.47 m

Now we need to find the time at which the two objects will meet. We can use the height of the first object at the time the second object is launched, and the equation for free fall to find the time it takes for the first object to reach the height of the second object:

37.47 = 20.27 + 0 + (1/2)(-9.8)t^2

Solving for t, we find that the objects will meet at a time of approximately 1.47 seconds.

Finally, we can use this time to find the height at which they will meet:

h = 22.0 + 0 + (1/2)(-9.8)(1.47^2) = 37.47 m

So the objects will first meet at a height of 37.47 m above the ground.

The earthquake would occur 13 minutes before 10:05 a.m. which will be at 9.52 am.

The p-waves travel with a constant velocity of 7 km/s

The time can be calculated by using the formula

t = d / v

where

T1 =  10:05 a.m

d is the distance they take to travel from the epicenter

v is the speed of the p-waves

On average, the speed of p-waves is

v = 7 km/s

d = 5600 km (given)

Substituting the values in the formula;

t = d / v

t = 5600 ÷ 7

t = 800 seconds

Converting into minutes,

t = 800 ÷ 60

t = 13.3

≈ 13 mins

T1 -  13 mins = T2

10:05 - 13 mins = 9.52 am

It means the earthquake occurred prior 13 minutes, that is at 9.52 am.

Therefore, the earthquake occurred at 9.52 am.

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Answer:

If the heavy load had been lifted more slowly, the work done on the load would have been the same.

Explanation:

Work done on an object is given as;

W = Fd

where;

F is the force applied on the object

d is the displacement of the object

for the given question, the applied force on the load = mg (mass of the load multiplied by acceleration due to gravity).

Also, the displacement of the object = vertical height the load was lifted.

W = mgh

The work done on the load is independent of time.

Thus, if the heavy load had been lifted more slowly, the work done on the load would have been the same.

A person lifting a heavy load to a vertical height of 2.0 m in 3 seconds does the same work as if he/she lifts it in 6 s.

A person lifts a heavy load to a vertical height of 2.0 m in 3 seconds.

We want to compare the work done with the one that he/she would have done if the process had taken 6 seconds.

In physics, work (W) is the energy transferred to or from an object via the application of force (F) along a displacement (s).

W = F × s

Given the displacement is the same (2.0 m) and the force needed is also the same (weight of the object), the work is the same for both processes.

A person lifting a heavy load to a vertical height of 2.0 m in 3 seconds does the same work as if he/she lifts it in 6 s.

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c) 8

When you shake a rope, the particles in the rope move up and down, and the wave moves forward or away from the source of energy. The rope moves in a direction that is perpendicular

Nodes are the places where the rope doesn't move at all; antinodes occur where the motion is greatest.

Step 1

let's check the graph:

a) Nodes

and Antinodes

so, in the ripe there are 8 antinodes

therefore, the answer is

c) 8

I

Answer:

Below

Explanation:

a) To find the force of friction acting on the mass we can use this formula :

     friction = coefficientoffriction x normal force

First we need to find the normal force of this object :

     Fn = mg

          = (6.0)(9.8)

          = 58.8 N

Now we can find the force of friction acting on the object :

     friction = (0.20)(58.8N)

                 = 11.76 N

                 = 12 N (we round this to 2 sig figs)

b) To find the force needed to accelerate this object at 0.68 m/s^2 use this :

     F = ma

     0.68 = x - 11.76 / 6

     x = 15.84

     x = 16 N

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The displacement vectors in component form are A = 1.732 km i + 1 km j and B =  -2.955 km i - 0.522 km j.

The distance from home when cell phone rings is 1.309 km.

The direction from home when phone rings is 21.48° West of South.

(a) The displacement vector A can be expressed in component form as:

A = 2 km [cos(30°) i + sin(30°) j] = 2 km [√3/2 i + 1/2 j] ≈ 1.732 km i + 1 km j

The displacement vector B can be expressed in component form as:

B = 3 km [cos(280°) i + sin(280°) j] = 3 km [-0.985 i - 0.174 j] ≈ -2.955 km i - 0.522 km j

(b) The total displacement vector (C) is the sum of vectors A and B, which can be found by adding the corresponding components:

C = A + B = (1.732 - 2.955) km i + (1 - 0.522) km j = -1.223 km i + 0.478 km j

The magnitude of the resulting vector C can be found using the Pythagorean theorem:

|C| = √((-1.223)² + (0.478)²) ≈ 1.309 km

Therefore, you are about 1.309 km away from home when your cell phone rings.

(c) The direction of the resulting vector C can be found using the inverse tangent function:

θ = tan^-1(0.478/-1.223) ≈ -21.48°

Since the direction is measured with respect to the positive x axis, the direction from "home" to "you" when the phone rings is about 21.48° West of South.

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Answer:800 Joules

Explanation: Energy = Power × Time = 100∗8100∗8 = 800 joules

The z component of the angular momentum around the origin is 9 kg-m²/s.

Angular momentum is the property of any rotating object given by moment of inertia times angular velocity.

The z component of the angular momentum around the origin is is calculated as follows;

L = mvr

where;

v = ωr

where;

v = 12 rad/s x 0.5 m

v = 6 m/s

Substitute the given parameters' and solve for the z component of the angular momentum around the origin is;

L = (2 kg) x (6 m/s) x (0.75 m)

L = 9 kg-m²/s

Thus, the z component of the angular momentum around the origin is 9 kg-m²/s.

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Answer: 6.0

Explanation:

v = 0.5 * 12 = 6

l = m * r *v

l = 2 * 0.5 * 6

l= 6

Answer:

Explanation:

Check the diagram attached below for the diagram.

Let the weight of the rock be W and the mass of the meter stick be M. Note that the mass of the meter stick will be placed at the middle of the meter stick i.e at the 50cm mark

Using the principle of moment to calculate the weight of the rock. It states that the sum of clockwise moments is equal to the sum of anti clockwise moment.

Moment = Force * perpendicular distance

The meterstick acts in the clockwise direction while the rock acys in the anti clockwise direction

Clockwise moment = 1kg * 25 = 25kg/cm

Anticlockwise moment = W * 25cm = 25W kg/cm

Equating both moments of forces

25W = 25

W = 25/23

W = 1 kg

The mass of the rock is also 1 kg

Answer:

50 N

Explanation:

W = Fd

F = W/d

first convert cm → m:  50 cm x 1 m/cm = 0.50 m

F = (25 J) / (0.50 m) = 50 N

To find the speed of a star in which the hydrogen transition from level 2 to level 1 appears at wavelength 120.8 nm, we can use the Doppler effect. The Doppler effect states that the observed wavelength of light (λobs) emitted by a moving object will be shifted relative to its rest wavelength (λrest) by an amount proportional to the object's velocity (v) with respect to the observer:

λobs = λrest * (1 + v/c)

where c is the speed of light.

In this case, we can use the known rest wavelength of the transition (121.6 nm) and the observed wavelength (120.8 nm) to solve for the velocity:

120.8 nm = 121.6 nm * (1 + v/c)

Solving for v, we get:

v = c * (120.8 nm - 121.6 nm) / 121.6 nm = -12.5 * 10^5 m/s

This is the velocity of the star away from the observer.

To find the speed for a star in which this line appears at wavelength 121.1 nm, we can use the same formula:

v = c * (121.1 nm - 121.6 nm) / 121.6 nm = -2.5 * 10^5 m/s

To find the speed for a star in which this line appears at wavelength 121.8 nm, we can use the same formula:

v = c * (121.8 nm - 121.6 nm) / 121.6 nm = -0.8 * 10^5 m/s

The doppler effect is a physics phenomenon related to the perceived frequency variation of a moving wave relative to an observer.

This effect was studied by the Austrian physicist Christian Doppler (1803-1853) and the discovery was named after him. Hence, the doppler effect.

The doppler effect can be observed in any and all electromagnetic waves, such as light, or mechanical waves, such as sound.

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The acceleration due to gravity near the surface of the hypothetical planet is 3.02 m/s².

The formula for acceleration due to gravity is:

g = GM/r² Where, g = acceleration due to gravity G = universal gravitational constant M = mass of the planet r = radius of the planet

In this case, since the mass of the hypothetical planet is the same as that of Earth, we can use the mass of Earth instead of M.

Therefore, g is proportional to 1/r².

So, using the ratio of radii given (1.8), we can write:

r = 1.8 x r Earth, where r Earth is the radius of Earth.

Substituting this value of r in the formula for acceleration due to gravity, we get:

g = GM/(1.8 x r Earth)² = GM/(3.24 x rEarth²) = (1/3.24)GM/rEarth²

We know that the acceleration due to gravity on Earth (g Earth) is 9.8 m/s².

Therefore, we can calculate the acceleration due to gravity on the hypothetical planet (gh) as follows:

gh = (1/3.24) x g Earth = 3.02 m/s²

Thus, the acceleration due to gravity near the surface of the hypothetical planet is 3.02 m/s².

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Answer:

The higher the amplitude, the higher the energy.

The bag would move in the direction of the applied force.

What is the direction?

Recall that work is done when the force applied moves a distance in the direction of the force. In this case, we can see that the force was applied from the right. Do not also forget that the force applied must make the object to move in a given direction. The direction in which the acceleration is imparted must also be in the direction of the force.

The understanding of the impact of force on motion could be seen from the Newtons law. We know from the Newton’s law that an object would remain at rest or in  a state of uniform motion unless it I acted upon by an external force. This external force makes the object to move in the direction of the force.

Looking at the question, we are told that a 20 newtons is applied from the right hence, the bag would move in the direction of the applied force.

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Explanation:

Gravitational potential energy

= mgh

= (2kg)(10N/kg)(5m)

= 100J.

Answer:

\(\boxed {\boxed {\sf 100 \ Joules}}\)

Explanation:

Gravitational potential energy can be found using the following formula.

\(E_p=m*g*h\)

where m is the mass, g is the gravitational acceleration, and h is the height.

The mass of the ball is 2 kilograms, its height is 5 meters, and the acceleration due to gravity is 10 Newtons per kilogram.

\(m= 2 \ kg \\h= 5 \ m \\g= 10 \ N/kg\)

Substitute the values into the formula.

\(E_p=(2 \ kg)(10 \ N/kg)(5 \ m)\)

Multiply the first 2 numbers. The kilograms (kg) will cancel out when multiplying.

\(E_p=(20 \ N)(5 \ m)\)

Multiply again.

\(E_p=100 \ N*m\)

\(E_p= 100 \ J\)

The gravitational potential energy of the ball is 100 Joules.

Answer: C. A large force over a long distance.

The velocity of this automobile as a function of time. At t = 5 seconds, the automobile is 90 meters from its initial position.

To determine the distance traveled by the automobile from its t = 0 initial position, we need to calculate the area under the velocity-time graph up to t = 5 seconds.

The graph shows the velocity of the automobile as a function of time. Let's assume that positive velocity represents forward motion, and negative velocity represents backward motion.

Since velocity represents the rate of change of displacement, the area under the velocity-time graph represents the displacement or distance traveled. In this case, the area will consist of two parts: the area above the x-axis (forward motion) and the area below the x-axis (backward motion).

To calculate the area, we can break it down into two separate integrals:

1. The area above the x-axis (forward motion):

Since the velocity is constant at 20 m/s for the first 4 seconds, the area is a rectangle:

Area1 = velocity * time = 20 m/s * 4 s = 80 m

2. The area below the x-axis (backward motion):

The velocity changes to -10 m/s at t = 4 seconds. From t = 4 seconds to t = 5 seconds, the velocity is -10 m/s. The area is a rectangle:

Area2 = velocity * time = -10 m/s * 1 s = -10 m

To find the total distance traveled, we add the absolute values of the areas:

Total distance = |Area1| + |Area2| = |80 m| + |-10 m| = 80 m + 10 m = 90 m

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Answer:

True

Explanation:

This is because to know how someone behaves, they have to perform a particular action.

Answer:

It is Newton's first law of motion also referred  to as the law of inertia.

Explanation:

Answer:

capacitive reactance equals inductive reactance

The charge q(t) on the capacitor would be, \(q(t)= 0.25c(1-e^{-t/0.04s})\)

And the current I(t) in the circuit will be,\(I(t)= 0.25mA(1-e^{-t/0.04s})\)

To find the charge q(t) on the capacitor at any time t, we can use the equation for the charge on a capacitor in an RC circuit:

\(q(t)= Q_{max} (1-e^{-t/RC})\)

where Qmax is the maximum charge on the capacitor, R is the resistance, C is the capacitance, and t is time.

To find Qmax, we can use the equation for the maximum charge on a capacitor in an RC circuit:

Qmax = E × C

where E is the electromotive force.

So, we have:

Qmax = 100 V × 10⁻⁴F = 0.01 C

Using the given values of R and C, we have:

R*C = 400 ohms × 10⁻⁴F = 0.04 s

Substituting these values into the equation for q(t), we get:

\(q(t)= Q_0.01(1-e^{-t/0.04C})\)

To find the current I(t), we can use Ohm's law and the equation for the charge on a capacitor:

I(t) = (1/R) × d(q(t))/dt

where d(q(t))/dt is the derivative of q(t) with respect to time.

Taking the derivative of q(t), we get:

\(dq(t)/dt= 0.01C (1-e^{-t/0.04C})\)

Substituting this into the equation for I(t), we get:

\(I(t)= (1/400ohm)(0.01/0.04s) (1-e^{-t/0.04C})\)I

Simplifying, we get:

\(I(t)= 0.25mA(1-e^{-t/0.04C})\)

Therefore, the charge q(t) on the capacitor is:

\(q(t)= 0.25c(1-e^{-t/0.04s})\)

And the current I(t) in the circuit is:

\(I(t)= 0.25mA(1-e^{-t/0.04s})\)

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Answer: 250

Explanation:

By supplying the fundamental knowledge required to create new instruments and techniques for medical use, physics enhances our quality of life

From can openers, light bulbs, and mobile phones to muscles, lungs, and brains; from paintings, piccolos, and pirouettes to cameras, vehicles, and cathedrals; from earthquakes, tsunamis, and storms to quarks, DNA, and black holes, physics aids us in understanding the workings of the world around us.

The science of physics is the most fundamental and has many applications in contemporary technology. Because it makes it possible for smartphones, computers, televisions, watches, and many other modern technologies to function automatically, physics is crucial to modern technology.

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Answer:

Impulse = \(206.28 * 10 = 2062.8\) g.m/s

Explanation:

Impulse is equal to the product of force and time

Here

Density of car =  \(0.54\)  g/mL

Volume of car \(= 38.2\) mL

Mass of the car is equal to the product of density and volume of car

Mass of the car \(= 0.54 * 38.2\) \(= 20.628\) grams

Acceleration of the car is \(10\) m/s^2

Force is equal to product of mass and acceleration

F = \(20.628 * 10 = 206.28\) g .m/s^2

Impulse = F * t

Impulse = \(206.28 * 10 = 2062.8\) g.m/s

The average acceleration of the motorcycle over the given distance is approximately 9.39 m/s².

To calculate the average acceleration of the motorcycle, we can use the formula:

Average acceleration = (final velocity - initial velocity) / time

First, let's convert the final velocity from km/h to m/s since the distance is given in meters. We know that 1 km/h is equal to 0.2778 m/s.

Converting the final velocity:

Final velocity = 78 km/h * 0.2778 m/s = 21.67 m/s

Since the motorcycle starts from rest (initial velocity is zero), the formula becomes:

Average acceleration = (21.67 m/s - 0 m/s) / time

To find the time taken to reach this velocity, we need to use the formula for average speed:

Average speed = total distance/time

Rearranging the formula:

time = total distance / average speed

Plugging in the values:

time = 50 m / 21.67 m/s ≈ 2.31 seconds

Now we can calculate the average acceleration:

Average acceleration = (21.67 m/s - 0 m/s) / 2.31 s ≈ 9.39 m/s²

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