Physics homework help: A boat leaves the shore with a velocity of 5 mi/h at

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an angle of...? A boat leaves the shore with a velocity of 5 mi/h at an angle of 57 degrees north of east relative to the water. The river is 0.725 mi wide and carries an eastward current of 0.825 mi/h. How far downstream are they when they reach the opposite shore?
 
First, you need to calculate how long the boat's journey will be.
57 deg. north of east is 33 deg. compass. Disregard the current.
The river is .725 miles wide. So sketch a right angled triangle, with a 33 deg. angle and a known side length of .825 miles.
Tan 33 deg= .6494. so .6494 x .825 = .536 miles length for the opposite side.
Now Pythagoras. Work out the length of the hypotenuse.
sqrt .725^2 + .536^2 = 0.9 miles.
It would take the boat 1/5th of an hour to do 1 mile, so .9 miles would take 0.18 hours.
Now, the current. For a start, it will not affect the time taken! But, in the .18 hours, the water will carry the boar further downstream by 0.1485 miles. So add this to the previous 0.536 miles, and the boat will be 0.6845 miles east of its departure point at the far side.
 
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