Question

Find an expression, in closed form, for the total vertical distance the ball has traveled when it hits the floor for the nth time.

a) 4 * g * h / k
b) 2 * g * h / k
c) g * h / k
d) 8 * g * h / k

Answer 1

The expression for the total vertical distance the ball has traveled when it hits the floor for the nth time is 2 * g * h / k. The correct answer is option B.

Step-by-step explanation:

To find the expression for the total vertical distance the ball has traveled when it hits the floor for the nth time, we can use the equation for the total distance traveled by the ball. Since the ball travels up and down, the total distance is equal to twice the maximum height it reaches.

Using the equation h = 2g, where h is the maximum height and g is the acceleration due to gravity, we can substitute this into the expression and get the answer. Therefore, the correct option is b) 2 * g * h / k.