A 95 g tennis ball is traveling at 106 km/h when it bounces of a wall and travels in the opposite direction it came from at a speed of 88 km/h.

a. Determine the impulse on the ball if the. (don’t forget that it is a vector)
b. If the average force exerted on the ball by the wall is 450 N, determine the time the ball stayed in contact with the wall.

To determine the impulse on the tennis ball, we need to first calculate the change in momentum of the ball during the collision with the wall. Impulse is defined as the change in momentum, and momentum is the product of mass and velocity.

a. The formula for impulse is: impulse = change in momentum

To find the change in momentum, we need to calculate the initial momentum (before the bounce) and the final momentum (after the bounce).

Initial momentum (before the bounce):
The mass of the tennis ball is given as 95 g, which is equal to 0.095 kg. The initial velocity is 106 km/h, but we need to convert it to m/s to be consistent with the units of impulse.

Using the conversion factor 1 km/h = 0.2778 m/s, we can convert the initial velocity as follows:

Initial velocity = 106 km/h * 0.2778 m/s per km/h = 29.4444 m/s

Therefore, the initial momentum (P1) can be calculated as:

P1 = mass * initial velocity = 0.095 kg * 29.4444 m/s

Final momentum (after the bounce):
The final velocity is given as 88 km/h, which needs to be converted to m/s using the same conversion factor:

Final velocity = 88 km/h * 0.2778 m/s per km/h = 24.4444 m/s

Therefore, the final momentum (P2) can be calculated as:

P2 = mass * final velocity = 0.095 kg * 24.4444 m/s

Now, we can calculate the change in momentum by subtracting the initial momentum from the final momentum:

Change in momentum = P2 - P1

b. To determine the time the ball stayed in contact with the wall, we can use the formula for average force:

Average force = impulse / time

Rearranging the formula, we have:

Time = impulse / average force

Substituting the values we calculated for impulse and average force, we can find the time.