Based on Example 3.6, develop a script to produce an animation of a bouncing ball where ν₀ = 5 m/s and θ₀ = 50°. To do this, you must be able to predict exactly when the ball hits the ground. At this point, the direction changes (the new angle will equal the negative of the angle at impact), and the velocity will decrease in magnitude to reflect energy loss due to the collision of the ball with the ground. The change in velocity can be quantified by the coefficient of restitution C_R which is equal to the ratio of the velocity after to the velocity before impact. For the present case, use a value of C_R 0.8.

Example 3.6

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In the absence of air resistance, the Cartesian coordinates of a pro- jectile launched with an initial velocity (vo) and angle (0) can be computed with x = vo cos(0)t y = vo sin(e)t -0.5gt where g = 9.81 m/s. Develop a script to generate an animated plot of the projectile's trajectory given that vo = 5 m/s and 0 = 45.