Question

A car travels due east with a speed of 50.0 km/h50.0 \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 60.060.0^{\circ} with the vertical. Find the velocity of the rain with respect to (a) the car

Solution

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Answered 1 year ago
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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

vAB=vAEvBEv_{AB}=v_{AE}-v_{BE}

where AA is the first object, BB is the second object and EE is the Earth. In our case, this equation can be rewritten as

vrc=vrEvcEv_{rc}=v_{rE}-v_{cE}

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

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