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## Homework Statement

Consider there is a window 5 meters from a person. The window is sized 1.21 meters (4 ft) in length and .914 meter (3 ft) wide at a height of 6 meters from the ground.

A person 1.8288 meters tall (6 ft) wants to bounce a ball (COR: 0.789) on the ground such that the ball goes through the window on the first bounce.

If the person bounces the ball with a speed of 25m/s at an angle of -60° from the horizontal at a point in the middle (between him and the wall), calculate and plot the trajectory of the ball.

Will the ball go through the window? If not, change one of the values such that it does. Then find a RANGE of velocities that will meet this condition, while keeping the COR, Distance, and angle the same.

## Homework Equations

X0(t) = V0cos(theta)t

Y0(t) = V0sin(theta)t - g/2t^2

V = V0(alpha)^n : alpha = the COR, n = the bounce

## The Attempt at a Solution

I formulated an excel sheet to calculate where the ball was at 5 meters along the x direction and discovered that it was too high of a position and would hit above the window. After changing the velocity to 20 m/s it seems to work.

My problem is writing this in a simplistic formula. As well, finding the range of available velocities without having to use an excel spreed sheet for each calculation by "guessing" and trying each available velocity until i find a max and min.

Thanks for any support in this!!! <3