A ball thrown up falls back to the floor and bounces many times. For a ball thrown up in the direction shown in the figure, the position of the ball as a function of time is given by:

The velocities in the x and y directions are constants throughout the motion and are given by vx = v0sin(θ)cos(α) and vy = v0sin(θ) sin(α). In the vertical z direction the initial velocity is vz = v0cos(θ), and when the ball impacts the floor its rebound velocity is 0.8 of the vertical velocity at the start of the previous bounce. The time between bounces is given by tb = (2vz)/g, where v is the vertical component of the velocity at the start of the bounce. Make a 3-D plot (shown in the figure) that shows the trajectory of the ball during the first five bounces. Take Vo = 20 m/s, θ = 30°, α = 25°, and g = 9.8 m/s2.

Vo 10 150 100 100 y (m) 50 50 x (m)