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Question

A car is driving down the road at a velocity Vc relative to ground and is delivering newspapers to homes. The newspapers are thrown at a velocity of Vp relative to the car. At what angle θ must the newspaper be thrown, relative to the car, so that they fly in a direction parallel to the driveways?

A
θ=sin1(Vc/Vp)
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B
θ=sin1(Vp/Vc)
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C
θ=cos1(Vc/Vp)
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D
θ=cos1(Vp/Vc)
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Solution

The correct option is A θ=sin1(Vc/Vp)
For the newspapers to fly parallel to the driveways when they are airborne, the component of velocity of Vp that is parallel to the road must cancel out with Vc, so that the velocity of the newspaper with respect to ground is in a direction parallel to the driveways.

Vcar=Vc^i
Vnewspaper,car=VPcosθ^jVPsinθ^i
Let the velocity of newspaperVN w.r.t ground is in the direction of the driveway.
Vnewspaper,car=VNVcar
VPcosθ^jVPsinθ^i=VN^jVc^i
The component along the road must be zero.
Therefore, VPsinθ=Vc
θ=sin1(Vc/Vp)

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