Question

An astronaut stands by the rim of a crater on the Moon, where the acceleration of gravity is 1.62 m/s2 and there is no air. To determine the depth of the crater, she drops a rock and measures the time it takes for it to hit the bottom. If the depth of the crater is 120 m, how long does it take for the rock to fall to the bottom of the crater

Answer 1

12.1 seconds

Step-by-step explanation:

t = Time taken

u = Initial velocity

v = Final velocity = 0

s = Displacement = 120 m

a = Acceleration due to gravity on Moon = 1.67 m/s²

Equation of motion

`v^2-u^2=2as\\\Rightarrow -u^2=2as-v^2\\\Rightarrow -u^2=2* -1.67* 120-0^2\\\Rightarrow u=√(2* 1.67* 120)\\\Rightarrow u=20.02\ m/s`

`v=u+at\\\Rightarrow t=(v-u)/(a)\\\Rightarrow t=(0-20.2)/(-1.67)\\\Rightarrow t=12.1\ s`

Time taken by the rock to hit the bottom of the crater is 12.1 seconds