Question

a rock thrown vertically from the surface of the moon at a velocity of 24m/sec reaches a height of s=24t-o.8^2 meters in t seconds
a)find the rocks velocity and acceleration as a function of time
b) how long did it take the rock to reach its highest point?
c) how high did the rock go?
d) how long did it take the rock to reach half its maximum height?
e) how long was the rock aloft?
f)find the rocks speed when hitting the moon

Answer 1

a) and b)\[s(t) =24t-0.8^2,~~~v=\frac{ dx}{ dt } (24t-0.8t^2) \implies v = 24 -1.6t\]
Taking the derivative of displacement gives us velocity, so setting v = 0 and solving for t gives us the highest point.
\[0 = 24-1.6t \implies t=\frac{ 24 }{ 1.6 } = ?\]
c) Once you find t, plug it into your original displacement equation.
The rest should be fairly simple as well.