Question

The weight of a person on a plannet A is about half that on the Earth. He can jump upto 0.4 m height on the surface of the Earth. How high can be jump on the planet A ?

Answer 1

Weight of the person on a planet `A, W_A = mg_A`
Weight of the person on Earth, `W_E = mg_E ("as mass of the person is the same on the planet A and the Earth")`
We are given that `W_A = (1)/(2)W_E, mg_A = (1)/(2)mg_E or g_A = (1)/(2)g_E`
Let `h_A, h_E` be the heights to which the person can jump on the planet A and the Earth respectively.
Gain in PE on jumping on planet `A = mg_A h_A`
Gain in PE on jumping on Earth ` = mg_E h_E`
Since gain in potential energy by the person is the same in both the cases as the muscular effort of the person remains unaffected by the change is planets,
`mg_A h_A = mg_E h_E`
or `h_A = (g_Eh_E)/(g_A) = (g_E h_E)/((1)/(2)g_E) = 2h_E`
As `h_E = 0.4 m, h_A = 2 (0.4 m) = 0.8m`