Final answer:
a) The potential energy of the ball before the fall is 1.764 J. b) The kinetic energy of the ball as it hits the plate cannot be determined. c) The velocity of the ball on hitting the plate is approximately 8.71 m/s. d) The kinetic energy of the plate on the rebound depends on the velocity of the ball. e) The velocity of the rebound is approximately 5.54 m/s.
Step-by-step explanation:
a) The potential energy of the ball before the fall can be calculated using the formula: Potential energy = mass * gravity * height. Since the mass is given as 100g and the height is 1.8m, and the acceleration due to gravity is 9.8 m/s², we can plug in the values to get: Potential energy = 0.1 kg * 9.8 m/s² * 1.8 m = 1.764 J.
b) The kinetic energy of the ball as it hits the plate can be calculated using the formula: Kinetic energy = 0.5 * mass * velocity^2. Since the height of the rebound and the velocity on hitting the plate are not given, we cannot determine the kinetic energy at this point.
c) The velocity of the ball on hitting the plate can be found using the conservation of mechanical energy. The potential energy before the fall is equal to the kinetic energy on hitting the plate. Using the formula: Potential energy = Kinetic energy, we can solve for the velocity by rearranging the formula: velocity = sqrt(2 * gravity * height) = sqrt(2 * 9.8 m/s² * 1.8 m) ≈ 8.71 m/s.
d) The kinetic energy of the plate on the rebound can be calculated using the same formula as in part b. However, since the height of the rebound is given as 1.25m, we can plug in the values to get: Kinetic energy = 0.5 * mass * velocity^2 = 0.5 * 0.1 kg * velocity^2.
e) The velocity of the rebound can be found using the same formula as in part c, but with the height of the rebound. So we have: velocity = sqrt(2 * gravity * height) = sqrt(2 * 9.8 m/s² * 1.25 m) ≈ 5.54 m/s.