A toy boat can travel at 10 ft/s in still water. The child playing with the boat

Question

A toy boat can travel at 10 ft/s in still water.  The child playing with the boat wishes to send it across a 35 ft. wide stream that is flowing at 7 ft/s as shown.  If the child puts the boat in the stream at O without giving it any other motion besides its motor and keeps its orientation in the y direction, determine the position of point A where the boat hits the far shore if the boat cruises at top speed.  Also determine how much time it takes the boat to reach A.

Answers: x=24.5 ft, t=3.5 sec  

A toy boat can travel at 10 ft/s in still water. The child playing with the boat wishes to send it across a 35 ft. wide stream that is flowing at 7 ft/s as shown. If the child puts the boat in the stream at O without giving it any other motion besides its motor and keeps its orientation in the y direction, determine the position of point A where the boat hits the far shore if the boat cruises at top speed. Also determine how much time it takes the boat to reach A.

Explanation / Answer

tan(theta)= AM/OM

10/7= 35/OM

so, OM=24.5ft,

here, M is a point prependicularly doonward on lower part of river

b)Net velocity in horizantal direction= 7+10cos(90)= 7ft/sec

so, t= OM/ v= 24.5/7=3.5sec

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