Question

A car travels due east with a speed of $50.0 \mathrm{~km} / \mathrm{h}$. Rain is falling vertically with respect to Earth. The traces of the rain on the side windows of the car make an angle of $60.0^{\circ}$ with the vertical. Find the velocity of the rain with respect to (a) the car

Solution

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The equation that we use when we have two objects moving in relative velocity and being observed from the ground is

$v_{AB}=v_{AE}-v_{BE}$

where $A$ is the first object, $B$ is the second object and $E$ is the Earth. In our case, this equation can be rewritten as

$v_{rc}=v_{rE}-v_{cE}$

where $v_{rc}$ is the velocity of the rain relative to the car, $v_{rE}$ the velocity of the rain as observed from the ground, and $v_{cE}$ is the velocity of the car relative to the ground.