The acceleration due to gravity at the surface of Moon is 1.67 m/s^2. If a stone is thrown upward with a speed of 10 m/s, find

Question

1) the time required to reach the highest point

2) the maximum height reached by the stone

3) the speed of the stone at t = 8 s

4) the displacement of the stone at t = 8 s.

Answer 1

h(t) =-1.67t^2/2 + 10t

h'(t) = -1.67t + 10 = 0

t =10/1.67 seconds to reach max height = close to 6 seconds

max height = h(10/1.67) = -1.67(10/1.67)^2/2 + 10(10/1.67) meters =50(1.67)= 83.5 meters

at 8 seconds speed = h'(8) = -1.67(8) + 10= about -3.36 m/sec

displacement at 8 seconds = h(8) = -1.67(8)^2/2 + 10(8) =26.56 meters