Question

A fully dressed astronaut, weighing 1.2 × 103 N on Earth, is about to
jump down from a space capsule that has just landed safely on
Planet X. The drop to the surface of X is 2.8 m, and the astronaut’s
gravitational potential energy relative to the surface is 1.1 × 103 J.
(a) What is the magnitude of the gravitational field strength on
Planet X?
(b) How long does the jump take?
(c) What is the astronaut’s maximum speed?

Answer 1

The astronaut's weight on earth is
\[ W_{earth} = mg_{earth} \] where \( g_{earth} \) is the gravitational acceleration on earth.

Further, the gravitational potential energy, PE, is
\[ PE = mg_Xh \]
where \( g_X \) is the gravitational acceleration this planet, not the \( g_{earth} \) on earth.

Now you are told the values of \( W, PE \) and \( h \). From these you can deduce \( g_X \); that's part a.

Once you know the value of that acceleration, you can use the usual kinematic equations replacing the acceleration \( a \) with \( g_X \).

Make sense?