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Derive the closed form vertical distance equation for a bouncing ball, considering factors such as gravity and elasticity.

User Melegant
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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.

User NexAddo
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