First slide

Motion in a plane

Question

A motor boat travels certain distance down stream in 1 hr and up stream in 3 hrs. Now the angle normal to the flow at which the same boat must be rowed with same velocity in the river in order to cross the river along the least path is

Moderate

A

60º down stream
B

30º up stream
C

30ºdown stream
D

60º up stream

Solution

if time taken in downstream is 1 hr for a distance d then $(v_{R} + v_{b}) 1 = d$ where $v_{R} a n d v_{b}$ are the velocity of the river and man respectively/
for upstream $(v_{b} - v_{R}) 3 = d$ solving we get $v_{b} = 2 v_{R}$ for crossing the river in shortest path $v_{b r} \sin θ = v_{R}$
sin $θ$ = $\frac{1}{2}$ $θ = 30^{0}$

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