Question

A tennis ball bounces on the floor three times. If each time it loses 11% of its energy due to heating, how high does it rise after the third bounce, provided we released it 4.4 m from the floor?

Answer 1

h = 3.10 m

Step-by-step explanation:

As we know that after each bounce it will lose its 11% of energy

So remaining energy after each bounce is 89%

so let say its initial energy is E

so after first bounce the energy is

`E_1 = 0.89 E`

after 2nd bounce the energy is

`E_2 = 0.89(0.89 E)`

After third bounce the energy is

`E_3 = (0.89)(0.89)(0.89)E`

here initial energy is given as

`E = mgH_o`

now let say final height is "h" so after third bounce the energy is given as

`E_3 = mgh`

now from above equation we have

`mgh = (0.89)(0.89)(0.89)(mgH)`

`h = 0.705H`

`h = 0.705(4.4 m)`

`h = 3.10 m`