Question

A ball is dropped from a height of 10 m. If the energy of the ball reduces by 40% after striking the ground, how much height can the ball bounce back? (g = 10 m/s²)

(a) 2 m
(b) 4 m
(c) 6 m
(d) 8 m

Answer 1

The ball dropped from a height of 10 m can bounce back to a height of 6 m after losing 40% of its energy upon striking the ground, calculated using the conservation of energy principle.

Step-by-step explanation:

When a ball is dropped from a height of 10 m and loses 40% of its energy upon striking the ground, the height it can bounce back can be calculated using the conservation of energy principle. Initially, the ball has gravitational potential energy (GPE), which is completely converted into kinetic energy (KE) just before it hits the ground. The initial GPE is given by GPE = mgh, where m is the mass of the ball, g is the acceleration due to gravity, and h is the height from which the ball is dropped. After the collision, the remaining energy is 60% of the initial energy (100% - 40% loss), and this will be the GPE at the peak of the bounce back.

Mathematically, if the initial energy is E, then the energy after the bounce is 0.6E. As E is initially mgh, the height to which the ball can bounce back, denoted as h', can be found by equating the remaining energy to mgh':

0.6mgh = mgh'

Solving for h',

h' = 0.6 × h

h' = 0.6 × 10 m

h' = 6 m

Therefore, the ball can bounce back up to a height of 6 meters after losing 40% of its energy due to the impact with the ground.