Question

a tennis ball is on the top of a basketball. the basketball is then released on the ground which results the tennis ball being very high . the mass of the ball is 59g. find the max height of the tennis ball as it bounces .

use conservation of energy/momntum . kinetic enegy or gpe

please fraw a diagram

Answer 1

Given
a Basket ball and Tennis ball, let their masses are m1,m2
and m1 >>> m2

when the balls are released so that the basket ball reach first the ground and later the tennis ball

Let the initial velocities are V1i = V, V2i = -V before collision with basket ball

later after collision with basket ball the velocities are V1f = ? v2f =?

treating the collisions are elastic collisions

from the final velocities formulae

v1f = (2m2*v2i)/(m1+m2) + (m1-m2)V1i /(m1+m2)
and
V2f = (2m1*v1i)/(m1+m2) + (m2-m1)V2i /(m1+m2)

as m1>>>m2 then

v1f = (m1)(V1i)/m 1 =V1i = V

V2f = (2m1*V1i)/m1 + (-m1/m1)(-V2i) = 2*V + V = 3*V

V is the initial velocity of both balls

--- Using equations of motions

   V^2 - U^2 = 2ah

here the final velocity of the basket ball is zero so V = 0 and a = g (moving downward)

so    o- U^2 = -2gh
   h = u^2/2g = v^2/2g

for tennis ball

   V2i = 3*V, a = g

   o - (3V)^2 = 2*g*H

   H = 9V^2/2g

   H = 9(h)

so the tennis ball can reach a maximum height of 9 times the basket ball