To warm up for a match, a tennis player hits the 56.0 g ball vertically with her racket.

If the ball is stationary just before it is hit and goes 5.40 m high, what impulse did she impart to it?

(1/2) m v^2 = m g h

so
v = sqrt(2 g h)
impulse = m v = m sqrt(2 g h)
= 0.056 sqrt (2*9.81*5.40)

Well, it sounds like this tennis player really gave the ball a good whack! So let's calculate the impulse she imparted.

First, we need to find the initial velocity of the ball just before it was hit. Since it's being hit vertically, we know that the final velocity is zero when it reaches its highest point. Using the kinematic equation, Vf^2 = Vi^2 + 2ad, where Vf is the final velocity, Vi is the initial velocity, a is the acceleration, and d is the distance traveled, we can solve for Vi.

Since Vf is zero, the equation becomes 0 = Vi^2 + 2ad. Since the ball is only moving vertically, the distance traveled is twice the height it reaches, so d = 2 * 5.40 m = 10.80 m.

Now we can plug in the values: 0 = Vi^2 + 2 * 10.80 m * (-9.8 m/s^2). Solving for Vi, we find Vi = √(2 * 10.80 m * 9.8 m/s^2).

Finally, we can calculate the impulse using the formula I = m * ΔV, where I is the impulse, m is the mass of the ball, and ΔV is the change in velocity.

The change in velocity is the final velocity minus the initial velocity, which is 0 - Vi.

So the impulse is I = 0.056 kg * (-Vi).

And there you have it! The impulse the tennis player imparted to the ball is approximately 0.056 kg times the opposite of the initial velocity. Keep in mind that these calculations are based on assumptions, so don't take it too seriously, just like my tennis game!

To find the impulse imparted to the ball, we can use the principle of conservation of linear momentum. The impulse is defined as the change in momentum of the ball, which can be calculated using the equation:

Impulse = Final momentum - Initial momentum

Initially, the ball is stationary, so the initial momentum is zero. Finally, when the ball reaches its maximum height of 5.40 m, its vertical velocity would be zero, so the final momentum is also zero.

Therefore, the impulse imparted to the ball is:

Impulse = 0 - 0 = 0 kg·m/s

To find the impulse imparted to the ball by the tennis player, we can use the principle of conservation of momentum.

Impulse is defined as the change in momentum of an object. The momentum of an object can be calculated by multiplying its mass by its velocity.

In this case, the mass of the ball is given as 56.0 g, which is equivalent to 0.056 kg. Before the tennis player hit the ball, it was stationary, so its initial velocity was zero.

To calculate the final velocity of the ball, we can use the equation:

v^2 - u^2 = 2as

Where:
v = final velocity
u = initial velocity (which is 0 in this case)
a = acceleration due to gravity (9.8 m/s^2)
s = displacement (5.40 m)

Plugging in the values into the equation, we get:

v^2 - 0^2 = 2 * 9.8 * 5.40

v^2 = 2 * 9.8 * 5.40

v^2 = 105.84

v = √105.84

v ≈ 10.29 m/s

Now that we have the final velocity of the ball, we can calculate the momentum using the equation:

momentum = mass * velocity

momentum = 0.056 kg * 10.29 m/s

momentum ≈ 0.57 kg·m/s

Therefore, the impulse imparted to the ball by the tennis player is approximately 0.57 kg·m/s.