# Projectile Motion: How Fast can Sarah Throw the Ball?

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

After catching the ball, Sarah throws it back to Julie. The ball leaves Sarah's hand a distance 1.5 meters above the ground, and is moving with a speed of 16 m/s when it reaches a maximum height of 8 m above the ground.

## Answer:

Sarah throws the ball back to Julie with an initial speed of 24.8 m/s.

The question is about the speed at which the ball leaves Sarah's hand after she catches it. Using the provided information, we can calculate it with the physics of projectile motion.

If we assume the acceleration due to gravity (g) as -9.8 m/s², and the maximum height the ball achieves (H) as 8 m, we use the equation for the motion of objects under gravity, H = (V²sin²θ)/2g.

We know sin²θ is 1 when θ=90° (because Sarah throws the ball almost straight up to obtain a maximum distance). Therefore, if we solve the equation for V, the initial velocity or the speed of the ball as it leaves Sarah's hands, we get V = sqrt(2gH), which gives approximately 24.8 m/s.