Question

The weight of a person on planet A is about half that on the earth. He can jump up to 0.4 m in height on the surface of the earth. How high he can jump on planet A?

Answer 1

The weight of a person on a planet is half that on the earth,

W_A = `1/2 "W"_"E"`

or mgA = `1/2 "mg_E"`

or `"g"_A = 1/2 "g"_E`

Now, as the person jumps, gain in potential energy remains the same.

So, mg_Ah_A = mg_E h_E

∴ `"h"_A = ("g"_"E""h"_"E")/"g"_"A"`

= `("g"_"E" xx 0.4"m")/("g"_E/2)` (Using (I) nd h_E = 0.4 m)

= 0.8m

(Using (i) and h_E = 0.4 m)