I am in dire need of assistance.?

Mary needs to row her boat across a 160 m -wide river that is flowing to the east at a speed of 1.0 m/s . Mary can row with a speed of 2.6 m/s .

If Mary points her boat due north, how far from her intended landing spot will she be when she reaches the opposite shore?

What is her speed with respect to the shore?

1 Answer

  • 1 month ago

    Let me explain one way to think about it which may help.

    Imagine your are in your car on the road next to the river. Starting next to Mary, you drive at 1.0m/s east (same velocity as the water) while Mary rows.

    Relative to you (in your moving car) the water is not moving. And Mary appears to travel in a straight line north, directly away from you.

    She crosses the river which is 160m north at 2.6m/s.

    Time taken = distance/time = 160/2.6 = 61.54s

    But during this time you, the water and Mary have all moved at 1.0m/s east. So distance east moved = speed x time = 1.0 x 61.54 = 61.54m = 62m to 2 sig. figs.

    Her intended landing spot was the point due north of her start point.

    So she reaches her landing spot 62m east of her intended landing spot.

    To get speed relative to the shore, we have to use vector addition of 2 perpendicular vectors to add 1.0m/s due east and 2.6m/s due north:

    v = √(1.0² + 2.6²) = 2.8m/s

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