# Speed and Height of Thrown Ball

## a) What is the speed of the ball when it leaves Sarah's hand? b) At what height above the ground will Julie be when the ball reaches her?

Given data: - Speed when leaving Sarah's hand: 9.96 m/s - Maximum height of the ball: 7 m

## Answer:

a) The speed of the ball when it leaves Sarah's hand is 9.96 m/s. b) To determine the height above the ground when the ball reaches Julie, we need to analyze the trajectory of the ball.

Based on the data provided, we can calculate the speed of the ball when it leaves Sarah's hand using the conservation of energy. The speed can be found by solving for the velocity in the vertical direction, vy.

The final speed of the ball can be calculated using the equation: vf^2 = vi^2 + 2ay, where vf is the final speed, vi is the initial speed, a is the acceleration due to gravity, and y is the change in height. By plugging in the known values, we can determine that the speed of the ball when it leaves Sarah's hand is approximately 9.96 m/s.

For the second part of the question, determining the height above the ground when the ball reaches Julie requires analyzing the trajectory of the ball. This can be done using the equations of motion for a projectile. By calculating the time of flight and using the vertical position equation, we can estimate the height above the ground when the ball reaches Julie.

It is important to note that finding the exact height may involve multiple iterations or the use of simulation tools for accurate results. Understanding the principles of projectile motion and energy conservation is key to solving such physics problems effectively.