Question

Your spaceship lands on an unknown planet. To determine the local value of g, you ask a steel-toed crew member to kick a stone, and you find that if she kicks it at 18.0m/s at various angles, the maximum range she can achieve is 30.8m.

What is g on this planet?

How long was the stone in the air?

How high above the ground did the stone go?

Answer 1

Ok, you already know that an angle of 45 deg gives the max range.

In the vertical:
hf=hi+18sin45t-1/2 g t^2
but hi=hf so
t= 2*18sin45/g

in the horizontal

30.8=18cos45*t put t in and solve for g.