# Q & A: Balls thrown on earth and moon

Q:
a similar ball are thrown vertically each with a velocity 20 m/s one on the earth surface and other on the surface of moon what will be ratio of the maximum height attained by them
- Deepak (age 15)
Jaipur
A:

Each ball starts with some kinetic energy given by E = 1/2*m*v^2. That is, Energy is equal to one-half times the mass of the ball times the initial velocity of the ball squared.

The maximum height each ball will reach is determined by the height where all of the initial kinetic energy of the ball is converted into potential energy given by the formulate U = m*g*h, that is Potential energy is equal to the mass of the ball times the gravitational constant (which is different on the surface of the Moon and Earth) times the height of the ball.

So two balls which both start with the same kinetic energy on the Earth and the Moon will reach maximum heights which will simply be a ratio of the gravitational constants for the Earth and the Moon. g on the Earth is equal to 9.8 m/s^2 while g on the moon is equal to 1.6m/s^2, so the maximum height would be the ratio of these numbers, or approximately 6. So the same ball thrown on the Earth and Moon will go about 6 times higher on the moon.

Sheldon S.

(published on 08/08/2016)