A ball is dropped from a height of 10m .If the energy of ball reduces by 40% after striking the ground, how much high can the ball bounce back?
It can bounce back to 60% of the initial drop height. (6 meters)
please explain your answer @drwls numerically.
I did.
To find out how high the ball bounces back, we need to calculate the percentage of energy the ball retains after striking the ground.
Given that the energy of the ball reduces by 40% after striking the ground, we can say that the ball retains 100% - 40% = 60% of its initial energy.
Now, we can use the principle of conservation of mechanical energy to find the height to which the ball bounces back. The total mechanical energy (potential energy + kinetic energy) is conserved in an ideal situation without any energy losses due to friction or air resistance.
When the ball is at its highest point, all its initial potential energy is converted into kinetic energy. Similarly, at its lowest point (after striking the ground), all the initial kinetic energy is converted into potential energy.
Therefore, we can equate the initial potential energy to the final potential energy:
Initial Potential Energy = Final Potential Energy
At the initial stage, the potential energy of the ball is given by:
Initial Potential Energy = m * g * h
where,
m is the mass of the ball (we assume it to be constant),
g is the acceleration due to gravity (9.8 m/s^2),
h is the initial height (10 m).
At the final stage, after bouncing back, the potential energy of the ball is given by:
Final Potential Energy = m * g * H
where H is the height to which the ball bounces back.
Since the ball retains 60% of its initial energy after striking the ground, we can write:
Final Potential Energy = 0.60 * (Initial Potential Energy)
Substituting the values:
m * g * H = 0.60 * (m * g * h)
The mass (m) and acceleration due to gravity (g) are common on both sides of the equation, so we can cancel them out:
H = 0.60 * h
Therefore, the ball can bounce back to a height of:
H = 0.60 * 10 = 6 meters
Hence, the ball can bounce back to a height of 6 meters.