## Related questions with answers

When astronauts from the Apollo 15 spacecraft landed on the moon, one of the experiments they conducted was to test Galileo's theory that if two objects of different masses are in free fall in a vacuum, they will land at the same time, regardless of their weight. The moon was an ideal place to test this theory, since its gravitational pull is minimal and there is no air resistance. So, one of the astronauts let a hammer and a feather fall from his hands at about $1.22$ metres from the ground, and indeed they landed at the same time! The accele ration due to gravity on the moon is about $1.625 \mathrm{~ms}^{-2}$. This is far less than that on earth, which is about $9.8 \mathrm{~ms}^{-}$.

Write an equation relating an object's acceleration due to gravity on the moon with the rate of change of the object's velocity, $v$. Hence, find a formula for $v$ using the initial condition that at $t=0, v=0$.

Solution

VerifiedThe equation relating to the acceleration due to moon with the rate of change of the object's velocity can be obtained as,

$\begin{align*} \dfrac{dv(t)}{dt} & = 1.625\\ v(t) & = \int 1.625 dt\\ &= 1.625t + c \end{align*}$

where $c$ is the integrating constant.

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