Projectile Motion Problem: Speed of the Ball

What is the speed of the ball when it leaves Sarah's hand?

The speed of the ball when it leaves Sarah's hand is 25.33 m/s.

To determine the speed of the ball when it leaves Sarah's hand, we can utilize the kinematic equations for projectile motion. First, we need to find the horizontal distance the ball travels before reaching Julie's position. We know that the time it takes for the ball to reach the highest point is half of the total time, which is 1.408 seconds. Using this time and the acceleration due to gravity (9.81 m/s^2), we can calculate the vertical velocity at the highest point.

Next, we can use the maximum height (20 m) and the initial vertical velocity to find the initial vertical velocity. Afterward, we can use the given time the ball takes to reach Julie's position (2.816 s) and the horizontal distance to find the initial horizontal velocity.

By applying the Pythagorean theorem, we can find the initial speed of the ball. After performing the calculations, we find that the speed of the ball when it leaves Sarah's hand is 25.33 m/s.