A rock thrown vertically upward from the surface of the Moon

A rock thrown vertically upward from the surface of the Moon at a velocity of 30 m/sec reaches a height of s = 30t - 2.6t^2 meters in t sec. a) Find the rock\'s velocity and acceleration of gravity at time t (the acceleration in this case is the acceleration of gravity on the Moon, which is different than on Earth.) b) How long does it take the rock to reach its highest point? c) How high does the rock go?

Solution

4) we have given s=30t-2.6t^2

a) Velocity v(t)=ds/dt=30-5.2t m/s

acceleration a(t)=dv(t)/dt = -5.2 m/s^2

b) At highest point v(t)=0

30-5.2t=0

5.2t=30

t=30/5.2=5.7 seconds

it takes 5.7 seconds to reach the highest point

c) we have given s=30t-2.6t^2

substitute t=5.7 into s

s(5.7)=(30*5.7)-(2.6*(5.7)^2)=86.526 m

the rock goes 86.526 m high