When she sees the red traffic light, Marie brakes to a halt from a speed of 70m/s in just 2.0
seconds. What is her acceleration?

Answer:

22 m/s

Explanation:

We can use the principle of conservation of momentum to solve this problem. The equation for the conservation of momentum is:

m1v1 + I = m2v2

where m1 is the mass of the soccer ball (0.25 kg), v1 is the initial velocity (2 m/s), I is the impulse (10 N.s), m2 is the mass of the soccer ball (0.25 kg), and v2 is the final velocity (unknown).

We can rearrange the equation to solve for v2:

v2 = (m1v1 + I) / m2

Substituting the given values, we get:

v2 = (0.25 kg * 2 m/s + 10 N.s) / 0.25 kg

Simplifying the equation, we get:

v2 = (0.5 kg⋅m/s + 10 N.s) / 0.25 kg

v2 = 22 m/s

Therefore, the final velocity of the soccer ball is 22 m/s.

Answer:

66n

Explanation:

4376

Answer:

The distance traveled by the tuning fork is 9.37 m

Explanation:

Given;

source frequency, \(f_s\) = 683 Hz

observed frequency, \(f_o\) = 657 Hz

The speed at which the tuning fork fell is calculated by applying Doppler effect formula;

\(f_o = f_s [\frac{v}{v + v_s} ]\)

where;

\(v\) is speed of sound in air = 343 m/s

\(v_s\) is the speed of the falling tuning fork

\(657 = 683[\frac{343}{343 + v_s} ]\\\\\frac{657}{683} = \frac{343}{343 + v_s}\\\\0.962 = \frac{343}{343 + v_s}\\\\0.962(343 + v_s) = 343\\\\343 + v_s = \frac{343}{0.962} \\\\343 + v_s = 356.55\\\\v_s = 356.55 - 343\\\\v_s = 13.55 \ m/s\)

The distance traveled by the tuning fork is calculated by applying kinematic equation as follows;

\(v_s^2 = v_o^2 + 2gh\)

where;

\(v_o\) is the initial speed of the tuning fork = 0

g is acceleration due to gravity = 9.80 m/s²

\(v_s^2 = 0 + 2gh\\\\h = \frac{v_s^2}{2g} \\\\h = \frac{13.55^2 }{2\times 9.8} \\\\h = 9.37 \ m\)

Therefore, the distance traveled by the tuning fork is 9.37 m

Answer: Bohr developed the Bohr model of the atom, in which he proposed that energy levels of electrons are discrete and that the electrons revolve in stable orbits around the atomic nucleus but can jump from one energy level (or orbit) to another. ... During the 1930s Bohr helped refugees from Nazism.

Answer:

e

Explanation:

The terminal velocity of the sphere is approximately 22.68 mph.

The terminal velocity of a sphere is the constant speed at which the gravitational force pulling the sphere down is balanced by the drag force pushing the sphere up. The drag force is proportional to the velocity of the sphere, and can be calculated using the following formula:

Fd = (1/2) * rho * Cd * A * v²

where Fd is the drag force, rho is the density of the fluid (air in this case), Cd is the drag coefficient (which depends on the shape of the object), A is the cross-sectional area of the object perpendicular to the direction of motion, and v is the velocity of the object.

The gravitational force pulling the sphere down is given by:

Fg = m * g

where m is the mass of the sphere and g is the acceleration due to gravity.

At terminal velocity, the drag force is equal in magnitude to the gravitational force, so:

Fd = Fg

Substituting the expressions for Fd and Fg and solving for v, we get:

v = √((2 * m * g) / (rho * Cd * A))

where A = pi * r² is the cross-sectional area of the sphere, and r is the radius of the sphere.

Plugging in the given values, we get:

v = sqrt((2 * 0.6 * 9.81) / (1.2 * 0.47 * pi * 0.3²)) ≈ 10.13 m/s

To convert this to mph, we multiply by 2.23694:

v ≈ 22.68 mph

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if the values of mass (m) and radius (R) are provided, the moment of inertia of the body about an axis through the center of disk A can be calculated as (3/2) * m * R^2, and the kinetic energy of the rotating body would be 162 * m * R^2 Joules.

To calculate the moment of inertia of the body about an axis through the center of disk A, we need to consider the moment of inertia contributions from each individual disk and add them up.

Let's denote the moment of inertia of each disk as I_A, I_B, and I_C, respectively. The moment of inertia of a disk rotating about its center can be calculated using the formula:

I = (1/2) * m * r^2

Where m is the mass of the disk and r is its radius.

Since the struts have negligible weight, we can assume that each disk has the same mass.

Let's assume the mass of each disk is m and the radius of each disk is R.

The moment of inertia of disk A (I_A) is given by:

I_A = (1/2) * m * R^2

The moment of inertia of disk B (I_B) and disk C (I_C) will be the same since they have the same mass and radius:

I_B = I_C = (1/2) * m * R^2

The total moment of inertia of the body about the axis through the center of disk A (I_total) is the sum of the individual moment of inertias:

I_total = I_A + I_B + I_C

= (1/2) * m * R^2 + (1/2) * m * R^2 + (1/2) * m * R^2

= (3/2) * m * R^2

To calculate the kinetic energy of the rotating body, we can use the formula:

Kinetic Energy = (1/2) * I_total * ω^2

Substituting the given values:

Kinetic Energy = (1/2) * ((3/2) * m * R^2) * (6.0 rad/s)^2

Simplifying further, if the values of m and R are given, we can calculate the moment of inertia and kinetic energy.

Assuming that the values of mass (m) and radius (R) are given, we can calculate the moment of inertia (I_total) and kinetic energy.

For the given values of ω = 6.0 rad/s and the previously calculated I_total:

I_total = (3/2) * m * R^2

Kinetic Energy = (1/2) * I_total * ω^2

= (1/2) * [(3/2) * m * R^2] * (6.0 rad/s)^2

= (9/2) * m * R^2 * (36.0 rad^2/s^2)

= 162 * m * R^2 Joules

Therefore, if the values of mass (m) and radius (R) are provided, the moment of inertia of the body about an axis through the center of disk A can be calculated as (3/2) * m * R^2, and the kinetic energy of the rotating body would be 162 * m * R^2 Joules.

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Answer:

The right approach is "1479°C".

Explanation:

The given values are:

Mass of iron piece,

\(m_p=42 \ kg\)

Mass of iron bucket,

\(m_I=5 \ kg\)

Mass of water,

\(m_w=10 \ kg\)

Iron's specific heat,

\(C_I=470 \ J/Kg^{\circ}C\)

Water's specific heat,

\(C_w=4186 \ J/Kg^{\circ}C\)

Initial temperature,

\(t_I=23^{\circ}C\)

Final equilibrium temperature,

\(T=150^{\circ}C\)

Latent heat,

\(L_v=2260\times 10^3 \ J/Kg\)

As we know,

The heat lost by the glowing piece of iron will be equal to the heat gain by the iron bucket as well as water, then

⇒ \(m_IC_I \Delta T=m_wC_w(100-23)+m_wL_v+m_bC_I(150-23)\)

On substituting the given values, we get

⇒ \(42\times 420\times \Delta T=10\times 4186(100-23)+10(2260\times 10^3)+5\times 420(150-23)\)

⇒ \(17640 \Delta T=3.22\times 10^6+2.26\times 10^7+2.667\times 10^5\)

⇒          \(\Delta T=\frac{2.60867\times 10^7}{17640}\)

⇒          \(\Delta T=1479^{\circ}C\)

Answer:

Option A is the only valid statement.

Explanation:

A)The electric field intensity is defined by the relationship:

E= -ΔV/Δr.

Now, according to the relationship above, the electric field would be the negative gradient of electric potential. Now, if the electric potential is constant throughout the given region of space, then the change in electric potential would be ΔV=0.

Thu,E= 0.

So the answer is that, E will be zero in this case.

So, the statement is valid.

B) Statement not valid because the field is the gradient of the potential. Hence, the field would be zero in any region where the potential is constant. However, constant does not necessarily mean a value of zero. With that being said, we can always change the definition of the potential function by adding a constant, to thus make it zero there. But then the potential will no longer be zero at infinity or in any different “flat” regions.

C) Statement not valid because, for the fact that electric field is zero at a particular point, it doesn't necessarily

imply that the electric potential is zero at that point. A good example would be the case of two identical charges which are separated by some distance. At the midpoint between the charges, the

electric field due to the charges would be zero. However, the electric potential due to the charges at that same point would not be zero. Thus, the potential will either have two positive contributions, if the charges are positive, or two negative contributions, if the charges are negative.

(D) Statement is not valid because, for the fact that electric potential is zero at a particular point, it does not necessarily imply that the electric field is zero at that point. A good example would be the case of a dipole, which

has two charges of the same magnitude, but opposite sign, and are separated by some distance. At

the midpoint between the charges, the electric potential due to the charges would be zero, but the electric field due to the charges at that same point would not be zero.

Explanation:

T = 2π√(m/k)

T = 2π√(16 kg / 4 N/m)

T = 4π s

T ≈ 12.6 s

Answer:

Look down below

Explanation:

300Hz is the 5th harmonic in a 60 Hz system, or the 6th harmonic in a 50 Hz system.

a) The order in which the objects reach the bottom of the slope depends on their moments of inertia, b) All three shapes will reach the bottom of the slope in approximately the same amount of time, which is around 0.42 seconds, c) The solid cylinder has the greatest moment of inertia, d) All three objects have the same linear acceleration of approximately 1.52 m/s^2, and e) All three objects have the same tangential (linear) velocity of approximately 1.52 m/s.

A slope is a slanted surface that connects two different levels or elevations.

a) The order in which the objects reach the bottom of the slope depends on their moments of inertia. The object with the smallest moment of inertia will reach the bottom first, followed by the object with the next smallest moment of inertia, and so on.

b) The time it takes each shape to reach the bottom of the slope can be calculated using the formula:

t = sqrt(2h/(g*sin(theta)))

where h is the height of the slope (1 m), g is the acceleration due to gravity (9.81 m/s^2), and theta is the angle of the slope (20°).

For the given values, we have:

t_ring = sqrt(21/(9.81sin(20°))) ≈ 0.42 s

t_sphere = sqrt(21/(9.81sin(20°))) ≈ 0.42 s

t_cylinder = sqrt(21/(9.81sin(20°))) ≈ 0.42 s

Therefore, all three shapes will reach the bottom of the slope in approximately the same amount of time.

c) The moment of inertia of a ring, sphere, and solid cylinder can be calculated using the formulas:

I_ring = m*r^2

I_sphere = (2/5)mr^2

I_cylinder = (1/2)mr^2

where m is the mass of the object and r is its radius.

Since all three objects have the same mass and are made from the same material, their radii must be different in order for their moments of inertia to be different. Therefore, the object with the greatest radius will have the greatest moment of inertia. In this case, the solid cylinder has the greatest radius, so it has the greatest moment of inertia.

d) The linear acceleration of each object can be calculated using the formula:

a = gsin(theta)(1 - mu*cos(theta))

where mu is the coefficient of static friction between the object and the slope.

For the given values, we have:

a_ring = 9.81sin(20°)(1 - 0.3cos(20°)) ≈ 1.52 m/s^2

a_sphere = 9.81sin(20°)(1 - 0.3cos(20°)) ≈ 1.52 m/s^2

a_cylinder = 9.81sin(20°)(1 - 0.3*cos(20°)) ≈ 1.52 m/s^2

Therefore, all three objects have the same linear acceleration.

e) The tangential (linear) velocity of each object can be calculated using the formula:

v = r*omega

where omega is the angular velocity of the object, which can be calculated using the formula:

omega = a/r

where a is the linear acceleration of the object and r is its radius.

For the given values, we have:

v_ring = r*omega = r(a/r) = a ≈ 1.52 m/s

v_sphere = r*omega = r(a/r) = a ≈ 1.52 m/s

v_cylinder = r*omega = r(a/r) = a ≈ 1.52 m/s

So, all three objects have the same tangential (linear) velocity.

Therefore, a) The order in which the objects reach the bottom of the slope depends on their moments of inertia, b) All three shapes will reach the bottom of the slope in approximately the same amount of time, which is around 0.42 seconds, c) The solid cylinder has the greatest moment of inertia, d) All three objects have the same linear acceleration of approximately 1.52 m/s^2, and e) All three objects have the same tangential (linear) velocity of approximately 1.52 m/s.

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Option A) 3.9 km is the correct answer. the magnitude of Rhea's displacement vector is approximately 3.92 km.

In order to find out the magnitude of Rhea's displacement vector, we have to add up all of the displacement vectors.

Then we can use the Pythagorean theorem to calculate the magnitude of the resultant vector.

Since Rhea is first driving north for 2.4 km and then west for 3.1 km, we can represent her displacement vectors as follows: Δx = 0 km and Δy = 2.4 km for the first vector, and Δx = -3.1 km and Δy = 0 km for the second vector.

We can then add these vectors together by adding their components: Δx = 0 km + (-3.1 km) = -3.1 km and Δy = 2.4 km + 0 km = 2.4 km.

This gives us a resultant vector of -3.1 km east and 2.4 km north.

Using the Pythagorean theorem, we can find the magnitude of this vector: \(\sqrt{(\(-3.1 km)^{2} + (2.4 km)^{2} ) } = \sqrt{(9.61 + 5.76) km^{2} } = \sqrt{15.37 km^{2} } \approx 3.92 km.\)

Therefore, the magnitude of Rhea's displacement vector is approximately 3.92 km.

Therefore, option A) 3.9 km is the correct answer.

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a) The tension is 76.9 lb when the balloon rises with v=0.8t ft/s and b) The tension is 74.1 lb when the balloon descents with v = 0.4t ft/s.

Newton's second law, states that the net force on an object is equal to its mass times its acceleration.

We can apply Newton's second law to the man and the balloon separately to determine the tension in each of his hands.

a) The net force on the balloon is equal to its mass times its acceleration, which is given by:

F(b) = mg + ma = mg + m(dv/dt)

= mg + m(d/dt(0.8 ft/s)

= (mg + 0.8m)/2

= [150 lb + (150b/32 ft/s²)(0.8 ft/s)]/2

T = 76.86 lb or 76.9 lb

b) When the balloon descends with a velocity of 0.4t ft/s, its acceleration is -0.4 ft/s² (negative because it is descending).

The net force on the man is still equal to the tension in his hands, which we can call T. Therefore:

T = m(m) × g - F(b)

where m(b) is the mass of the balloon, r is its radius, and ρₐ is the density of air,.

T = 150 lb × 32.2 ft/s² - (4/3)πr³ × ρₐ × 0.4 ft/s²

Dividing the tension equally between the man's hands, we get:

T(h) = T/2 = 75 lb × 32.2 ft/s² - (2/3)πr³× ρₐ × 0.4 ft/s²

Substituting the value of r and ρₐ, we get:

T(h) = 74.1 lb

Therefore, the answer is option 4) a) T=76.9 lb, b) T=74.1 lb.

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1) The velocity of the pin after the collision is 107.4 m/s.

2) The velocity of the two cars as the collision is inelastic is 48.2 m/s.

We know that by the principle of the conservation of linear momentum, the momentum before Collison is equal to the total momentum after collision. Now we have to use this principle in the both questions that we have here.

1) Given that;

Total momentum before collision = Total momentum after collision

(41.7 * 59.1) + (4.17 * 0) = (41.7 * 48.35) + ( 4.17 * v)

We then have;

2464 + 0 = 2016 +  4.17v

2464 - 2016 = 4.17v

v = 2464 - 2016 /4.17

v = 107.4 m/s

2) Given that;

Total momentum before collision = Total momentum after collision

(51.3 * 50.1) + (100 * 47.2) = (100 +  51.3)v

2570 + 4720 = 151.3v

v = 2570 + 4720/151.3

v = 48.2 m/s

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Answer: C Adding salt to water increases the boiling point and decreases the freezing point

Explanation:

The net force on q₂ will be  1.07 x 10⁻² N, pointing to the left.

To find the net force on particle q₂, we need to calculate the force due to q₁  and q₃ individually and then add them up vectorially. We can use Coulomb's law to calculate the force between two point charges:

F = k × (q₁ × q₂) / r²

where F is the magnitude of the force, k is Coulomb's constant (k = 8.99 x 10⁹ Nm²/C²), q1 and q2 are the charges of the two particles, and r is the distance between them.

The force due to q₁ on q₂ can be calculated as:

F₁ = k × (q₁ × q₂) / r₁²

where r1 is the distance between q₁ and q₂ (r₁ = 0.180 m).

Similarly, the force due to q₃ on q₂ can be calculated as:

F₂ = k × (q₃ × q₂) / r₃²

where r₃ is the distance between q₂ and q₃ (r₃= 0.230 m).

The direction of each force can be determined by the direction of the electric field due to each charge. Since q₁ and q₃ have opposite signs, their electric fields point in opposite directions. Therefore, the force due to q₁ points to the left and the force due to q₃ points to the right.

To find the net force, we need to add up the forces vectorially. Since the forces due to q₁ and q₃ are in opposite directions, we can subtract the magnitude of the force due to q₃ from the magnitude of the force due to q₁ to get the net force on q₂:

Fnet = F₁ - F₃

Substituting the values we get:

Fnet = k × (q₁ × q₂) / r₁² - k × (q₃ × q₂) / r₃²

Plugging in the values we get:

Fnet = (8.99 x 10⁹ Nm²/C²) × [(9.33 x 10⁻⁶ C) × (4.22 x 10⁻⁶ C) / (0.180 m)² - (-8.42 x 10⁻⁶ C) × (4.22 x 10⁻⁶ C) / (0.230 m)²]

Fnet = 1.07 x 10⁻² N

Therefore, the net force on q₂ is 1.07 x 10⁻² N, pointing to the left.

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If a planet has an orbital eccentricity equal to 0.70, then its orbit is

Eccentricity is a measure of how squashed an ellipse is compared to a perfect circle.

The value of eccentricity ranges from 0 to 1, where 0 represents a perfect circle and 1 represents a parabolic orbit (which is not a closed orbit).

An eccentricity of 0.70 indicates that the planet's orbit is significantly elongated and not close to a perfect circle.

Therefore, the correct answer is - A very elongated ellipse.

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Answer:

4.9 km

Explanation:

\(\sqrt{4.2^2+2.6^2}=4.9 km\)

Answer:

a is the correct answer

Explanation:

did the test and got it r

Two objects are connected by a string passing over a frictionless pulley, the tension in the string is 5.0 N.

To calculate the amount of the system's acceleration, we must examine the forces acting on the objects.

Weight (mg) =  weight of object A × (9.8) = 20.58 N.

Kinetic friction force (f k): Object A is subjected to a kinetic friction force with a magnitude of 5.0 N. This force acts in the opposite direction of motion.

Force on B:

Weight (mg) = weight of object B x (9.8) = 32.34 N.

a. Tension in the string (T): String tension acts upward and is transmitted from item A.

Now, we have:

f k = T

T = f k = 5.0 N

So, tension is 5N.

b. Now, the magnitude of acceleration:

F_net = mg - T

F_net = (3.3 kg) × (9.8) - 5.0 N = 32.34 N - 5.0 N = 27.34 N

F_net = m_b × a

27.34 N = (3.3 kg) × a

a = 27.34 N / (3.3 kg) ≈ 8.29 m/\(s^2\)

Therefore, the magnitude of acceleration for the system is approximately 8.29 m/\(s^2\).

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Your question seems incomplete, the probable complete question is:

Two objects are connected by a string passing over a frictionless pulley. When the objects are in motion object A experiences a force of kinetic friction with a magnitude equal to 5.0 N. The mass of object A is 2.1 kg and the mass of object B is 3.3 kg.

Determine the magnitude of acceleration for the system.

Determine the magnitude of the tension in the string.

Answer:

Explanation:

Normal force of the surface on the box will be

N = mg - Fsinθ

Ν = 10(9.8) - 600sin37

N = -263

As normal force cannot be less than zero, the applied force lifts the crate off the surface.

Now it's just a matter of finding the acceleration

In the horizontal direction, the acceleration is

a = F/m

a = (600cos37) / 10

a =  47.9181... m/s²

the crate weight is mg = 10(9.8) = 98 N.

In the vertical direction the acceleration is

a = ((600sin37 - 98) / 10)

a = 26.3089... m/s²

total acceleration is

a = √(47.9181² + 26.3089²)

a = 54.6653... m/s²

s = ½at²

t = √(2s/a)

t = √(2(1.0)/54.6653)

t = 0.19127...

t = 0.19 s

Answer:

Hello i hope this helps you! Potential and Kinetic EnergyHold the car at the top of the ramp, and release to demonstrate the two main kinds of energy. Potential energy is placed into the car when it's lifted from the floor, and that energy is released as the car rolls down the ramp.

Explanation:

hope this helps

Answer:

the tension force of the string on the stone is 30 N

Option d) 30 N is the correct answer.

Explanation:

Given the data in the question;

mass m = 0.2 kg

radius r = 0.6 m

θ = 150 revolutions = 300π rad

time t = 60 seconds

we know that; Angular speed ω = θ / t

we substitute

ω = 300π / 60

ω = 5π rad

Linear speed of stone u = ω × r

we substitute

u = 5π × 0.6

u = 3π m/s

The tension force of the string on the stone is equal to centripetal force, which aid it move in circle;

so

T = mv² / r

we substitute

T = [ 0.2 × (3π)² ] / 0.6

T = 17.7652879 / 0.6

T = 29.6 ≈ 30 N

Therefore, the tension force of the string on the stone is 30 N

Option d) 30 N is the correct answer.

Answer:

Explanation:

Let mass of ice cube taken out be m kg .

ice will gain heat to raise its temperature from - 5.5° to 0° and then from 0° to 17° .

Total heat gained = m x 2.1 x 5.5 + m x 333 + m x 4.186 x 17

= (11.55 + 333 + 71.162 )m

= 415.712 m kJ

Heat lost by aluminium calorimeter

= .075 x .9 x 3  

= .2025 kJ

Heat lost by water

= .3 x 4.186 x 3

= 3.7674

Total heat lost

= 3.9699 kJ

Heat lost = heat gained

415.712 m = 3.9699

m = .0095 kg

9.5 gm .

Answer:

0.00954g or 9.5x\(10^{-3}\) kg

Explanation:

The only conversion that is needed is changing the heat of fusion of water from 333 kJ/kg to 333000 J/kg.

This is the condensed version of the equation needed for this problem: mcΔT + mL + mcΔT = mcΔT + mcΔT

This is the expanded version of the equation needed for this problem:

\(m_{ice}\)(\(c_{ice}\))(temperature of ice from -5.5°C to 0°C) + \(m_{ice}\)(L) + \(m_{ice}\)(\(c_{water}\))(temperature of water from 0°C to 17°C) = \(m_{water}\)(\(c_{water}\))(ΔT) + \(m_{aluminum}\)(\(c_{aluminum}\))(ΔT)

Use the equation to solve for the mass of ice:

m(2100)(5.5) + m(333000) + m(4186)(17) = 0.3(4186)(20-17) + 0.075(900)(20-17)

m [(2100x5.5) + 333000 + (4186x17)] = 3767.4 + 202.5

m(415712) = 3969.9

m = 0.00954g or 9.5x\(10^{-3}\) kg

Answer:

An electric field has a magnitude of 400 N/C and makes an angle

60

o

with the perpendicular to the surface of a flat surface of dimensions 30 cm by 20 cm. Calculate the electric flux through the surface.

Explanation:

Answer:

A. 450 N

B. 3240 J

C. 0.77 KW

Explanation:

From the question given above, the following data were obtained:

Height of one step = 20 cm

Number of steps = 36

Mass of runner = 45 kg

Time taken = 4.2 s

Next, we shall convert 20 cm to metre (m). This can be obtained as follow:

100 cm = 1 m

Therefore,

20 cm = 20 cm × 1 m /100 cm

20 cm = 0.2 m

Next, we shall determine the total height. This can be obtained as follow:

Height of one step = 0.2 m

Number of steps = 36

Total height =?

Total height = 36 × 0.2

Total height = 7.2 m

A. Determination of the runner's weight.

Mass of runner (m) = 45 kg

Acceleration due to gravity (g) = 10 m/s²

Weight (W) =?

W = m × g

W = 45 × 10

W = 450 N

B. Determination of the increase in the potential energy.

At the ground level, the potential energy (PE₁) is 0 J.

Next, we shall determine the potential energy at 7.2 m. This can be obtained as follow:

Mass of runner (m) = 45 kg

Acceleration due to gravity (g) = 10 m/s²

Total height (h) = 7.2 m

Potential energy at height 7.2 m (PE₂) = ?

PE₂ = mgh

PE₂ = 45 × 10 × 7.2

PE₂ = 3240 J

Final, we shall determine the increase in potential energy. This can be obtained as follow:

Potential energy at ground (PE₁) = 0 J

Potential energy at height 7.2 m (PE₂) = 3240 J

Increase in potential energy =?

Increase in potential energy = PE₂ – PE₁

Increase in potential energy = 3240 – 0

Increase in potential energy = 3240 J

C. Determination of the power.

Energy (E) = 3240 J

Time (t) = 4.2 s

Power (P) =?

P = E/t

P = 3240 / 4.2

P = 771.43 W

Finally, we shall convert 771.43 W to kilowatt (KW). This can be obtained as follow:

1000 W = 1 KW

Therefore,

771.43 W = 771.43 W × 1 KW / 1000 W

771.43 W = 0.77 KW

Therefore, her power is 0.77 KW

Answer:

Hi ??? what is your question

Answer:

The expansion of the universe has caused cosmic microwave background radiation to cool. As the universe expands, the radiation is stretched out, causing its wavelength to increase and its temperature to decrease. This phenomenon is known as cosmic microwave background radiation redshift.

the answer is D. It has caused it to red-shift.

Recall that

\(\|\mathbf u\times\mathbf v\|=\|\mathbf u\|\|\mathbf v\|\sin\theta\)

where \(\theta\) is the angle between the vectors \(\mathbf u\) and \(\mathbf v\). No need to actually compute the cross product.

We can find the angle between the vectors using the dot product formula,

\(\mathbf u\cdot\mathbf v=\|\mathbf u\|\|\mathbf v\|\cos\theta\)

\(\implies\theta=\cos^{-1}\left(\dfrac{(2\mathbf i+2\mathbf j-\mathbf k)\cdot(-\mathbf i+\mathbf k)}{\sqrt{2^2+2^2+(-1)^2}\sqrt{(-1)^2+1^2}}\right)=\cos^{-1}\left(-\dfrac1{3\sqrt2}\right)\)

Then

\(\|\mathbf u\times\mathbf v\|=3\sqrt2\sin\theta=\boxed{\sqrt{17}}\)

a.

The direction of the total momentum is 45°

The momentum of the first car is given by p = mv where m = mass of car = 1200 kg and v = velocity of car = 15 m/sj (since it moves due north).

So, p = mv

= 1200 kg × (15 m/s)j

= (18000 kgm/s)j

Also, the momentum of the identical car, p' = mv' where m = mass of car = 1200 kg and v' = velocity of car = (15 m/s)i (since it moves due east).

So, p' = mv'

= 1200 kg × (15 m/s)i

= (18000 kgm/s)i

So, the total momentum of the system P = p + p'

=  (18000 kgm/s)j +  (18000 kgm/s)i

=  (18000 kgm/s)i +  (18000 kgm/s)j

The direction of the total momentum of the system P is gotten from

tanФ = p'/p

= 18000 kgm/s ÷ 18000 kgm/s

= 1

Ф = tan⁻¹(1)

= 45°

The direction of the total momentum is 45°

b.

The magnitude of the total momentum of the system is 25455.84 kgm/s

The magnitude of the total momentum of the system P = √(p'² + p²)

= √[(18000 kgm/s)² + (18000 kgm/s)²]

= (18000 kgm/s)√(1 + 1)

= (18000 kgm/s)√2

= 25455.84 kgm/s

The magnitude of the total momentum of the system is 25455.84 kgm/s

Learn more about total momentum here:

https://brainly.com/question/25635296