Final answer:
The closed form vertical distance equation for a bouncing ball is derived by considering factors such as gravity and elasticity. It can be written as d = (v_0^2 / (2*g)) * (1 + sqrt(1 + (2*g*h) / v_0^2)), where d is the vertical distance, v_0 is the initial velocity of the ball, g is the acceleration due to gravity, and h is the initial height of the ball.
Step-by-step explanation:
Bouncing Ball Equation
The closed form vertical distance equation for a bouncing ball can be derived by considering factors such as gravity and elasticity. The equation can be written as:
d = (v_0^2 / (2*g)) * (1 + sqrt(1 + (2*g*h) / v_0^2))
Where d is the vertical distance, v_0 is the initial velocity of the ball, g is the acceleration due to gravity, and h is the initial height of the ball.