A boat, whose speed in still water is 2.50 m/s, must cross a 285-m wide river and arrive at a point 118m upstream from where it
starts. To do so, the pilot must head the boat at a 45.0 degrees upstream angle. What is the speed of the rivers current?
1 answer:
The figure shows the arrangement of system
The velocity of boat can be resolved in to two
Horizontal component = vcos θ = 2.50 cos 45 = 1.768 m/s
Vertical component = vsin θ = 2.50 sin 45 = 1.768 m/s
Due to horizontal component the boat arrive arrives upstream,
Total horizontal velocity = 1.768 - Vr, where Vr is the velocity of river.
Total time taken to cross the river = width of river/ Vertical component of velocity
t = 285/1.768 = 161.20 seconds
So 118 meter is traveled at a velocity of 1.768-Vr in 161.20 seconds
That is 118 = (1.768-Vr)*161.20
1.768 - Vr =0.732
Vr = 1.036 m/s
So velocity of river flow =1.036 m/s
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