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27 September, 12:38

Suppose a boat moves at 12.0 m/s relative to the water. If the boat is in a river with the current directed east at 2.50 m/s, what is the boat's speed relative to the ground when it is heading (a) east, with the current, and (b) west, against the current?

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  1. 27 September, 12:45
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    (a) 14.5 m / s

    (b) 9.5 m / s

    Explanation:

    (a) velocity of boat with respect to water

    V (b, w) = 12 i m/s

    Velocity of water with respect to ground

    V (w, g) = 2.5 i m/s

    By the formula of relative velocity

    Velocity of boat with respect to ground

    V (b, g) = V (b, w) + V (w, g)

    V (b, g) = 12 i = 2.5 i = 14.5 i m/s

    Magnitude of velocity of boat with respect to ground = 14.5 m/s along + X axis.

    (b) velocity of boat with respect to water

    V (b, w) = - 12 i m/s

    Velocity of water with respect to ground

    V (w, g) = 2.5 i m/s

    By the formula of relative velocity

    Velocity of boat with respect to ground

    V (b, g) = V (b, w) + V (w, g)

    V (b, g) = - 12 i = 2.5 i = - 9.5 i m/s

    Magnitude of velocity of boat with respect to ground = 9.5 m/s along - X axis.
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