A Machine Launches a Tennis Ball at an Angle of 45° with the Horizontal

Calculation of Total Horizontal Distance Traveled by the Tennis Ball

A machine launches a tennis ball at an angle of 45° with the horizontal. The ball has an initial vertical velocity of 9.0 meters per second and an initial horizontal velocity of 9.0 meters per second. The ball reaches its maximum height 0.92 second after its launch. We are neglecting air resistance and assuming the ball lands at the same height above the ground from which it was launched.

Elapsed Time

+0.92 s

Viy = 9.0 m/s
Launcher V = 9.0 m/s

Horizontal velocity and vertical velocity components are both 9.0 m/s. Now, we need to determine the total horizontal distance traveled by the tennis ball during the entire time it is in the air.

Final Answer

Given a horizontal velocity of 9.0 m/s and a total flight time of 1.84 s, the tennis ball would travel approximately 16.56 meters horizontally.

Explanation

The total horizontal distance traveled by a tennis ball during the entire time it is in the air is referred to as the range. By neglecting air resistance and considering the ball lands at the same height, we can use a simple formula to calculate the range: range = horizontal velocity * total time in the air.

Using the provided values, the horizontal velocity is 9.0 m/s. The total time in the air can be calculated as twice the time it takes for the ball to reach its maximum height since the ball takes the same time to ascend and descend. The ball reaches its maximum height 0.92 seconds after launch, resulting in a total time in the air of 1.84 seconds.

Therefore, the total horizontal distance (or range) can be calculated as follows: range = 9.0 m/s * 1.84 s = approximately 16.56 meters.

What is the total horizontal distance traveled by the tennis ball during the entire time it is in the air?

17 meters