I have already solved 2 out of 3 questions:
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 16.0 m/s at various angles, the maximum range she can achieve is 32.8 m.
1) Answer: g = 7.80 m/s
2) Answer: t = 2.90 s
3) How high above the ground did the stone go (in m)?
Thanks!
assume you know max range at 45 degree angle
Vi = 16 cos 45 = 11.3 up and also horizontal
max height at v = 0
0 = 11.3 -gt
gt = 11.3 at max height where x = 32.8/2 =16.4
16.4 = 11.3 t
t = 1.45 seconds to max height, twice that to max range so indeed 2.90 seconds to ground, check
g(1.45) = 11.3
g = 7.8 m/s^2 check
for max height use 1.45 seconds in
h = 11.3 t - .5(7.8) t^2
= 16.4 - 8.2 = 8.2 meters high