A rowboat crosses a river with a velocity of 3.58 mi/h at an angle 62.5° north of west relative to the water. The river is 0.870 mi wide and carries an eastward current of 1.25 mi/h. How far upstream is the boat when it reaches the opposite shore?
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we first find the time it takes the boat to cross the river; for this we need the component of motion of the boat across the river, or in the northern direction
the component of motion to the north is 3.58 sin 62.5 = 3.18mi/hr
therefore it takes t=0.87mi/3.18mi/hr = 0.27h to cross the river
the total eastward component of motion is
-3.58 cos 62.5 + 1.25 = -0.4 mi/hr
meaning the boat is moving against the current
in the 0.27 h it takes to cross the river, the boat will be -0.4mi/h*0.27h = -0.1 mi upstream
the minus sign indicates upstream
the component of motion to the north is 3.58 sin 62.5 = 3.18mi/hr
therefore it takes t=0.87mi/3.18mi/hr = 0.27h to cross the river
the total eastward component of motion is
-3.58 cos 62.5 + 1.25 = -0.4 mi/hr
meaning the boat is moving against the current
in the 0.27 h it takes to cross the river, the boat will be -0.4mi/h*0.27h = -0.1 mi upstream
the minus sign indicates upstream
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I don't remember the cos tan sin thing but the velocity doesn't seem relevant. I believe you can use sine law though (side angle side) that's all I can remember though.