Reference Frames and Relative Motion

AP Physics 1· difficulty 4/5

A boat moves at 4.04.0 m/s relative to water in a river flowing at 3.03.0 m/s. To cross straight to the opposite shore (perpendicular to flow), the boat must point at angle (relative to perpendicular) of approximately

  • A

    0°

  • B

    arcsin(3/4)=48.6°\arcsin(3/4) = 48.6° upstream

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  • C

    53°53° downstream

  • D

    arctan(3/4)=37°\arctan(3/4) = 37° upstream

Explanation

The boat's velocity component upstream must cancel the river's flow: vboatsinθ=vriverv_{boat}\sin\theta = v_{river}, so θ=arcsin(3/4)=48.6°\theta = \arcsin(3/4) = 48.6°.

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