Question

A ball rolls off a hoop's rim, falls from a height of 3.20 m to the court's floor, and then bounces up to a height of 1.60 m. (Assume up is positive.) Indicate the direction with the sign of your answers.

a) The initial velocity is ( -√2gh ), where ( g = 9.8 , textm/s^2 )
b) The initial velocity is ( +√2gh ), where ( g = 9.8 , textm/s^2 )
c) The final velocity is ( +√2gh ), where ( g = 9.8 , textm/s^2 )
d) The final velocity is ( -√2gh ), where ( g = 9.8 , textm/s^2 )

Answer 1

a) The initial velocity is (-√2gh), b) The initial velocity is (-√2gh), c) The final velocity is (+√2gh), d) The final velocity is (-√2gh)

Step-by-step explanation:

a) The initial velocity of the ball can be calculated using the formula v = √2gh, where v is the initial velocity, g is the acceleration due to gravity (9.8 m/s^2), and h is the initial height from which the ball falls. In this case, h = 3.20 m. Substituting the given values into the formula, we get v = √(2 * 9.8 * 3.20) = √(62.72) ≈ 7.92 m/s. Since the ball is falling downward, the initial velocity is negative. Therefore, the correct answer is (a) The initial velocity is (-√2gh).

b) The initial velocity of the ball can also be calculated using the formula v = -√2gh. Here, we have the same values for g and h as in part (a). Substituting them into the formula, we get v = -√(2 * 9.8 * 3.20) = -√(62.72) ≈ -7.92 m/s. The negative sign indicates that the ball is moving downward. Therefore, the correct answer is (b) The initial velocity is (-√2gh).

c) The final velocity of the ball can be calculated using the formula v = √2gh, where v is the final velocity, g is the acceleration due to gravity (9.8 m/s^2), and h is the final height to which the ball bounces. In this case, h = 1.60 m. Substituting the given values into the formula, we get v = √(2 * 9.8 * 1.60) = √(31.36) ≈ 5.60 m/s. Since the ball is bouncing upward, the final velocity is positive. Therefore, the correct answer is (c) The final velocity is (+√2gh).

d) The final velocity of the ball can also be calculated using the formula v = -√2gh. Here, we have the same values for g and h as in part (c). Substituting them into the formula, we get v = -√(2 * 9.8 * 1.60) = -√(31.36) ≈ -5.60 m/s. The negative sign indicates that the ball is moving downward. Therefore, the correct answer is (d) The final velocity is (-√2gh).