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Question

A boat B is moving upstream with velocity 3 m/s with respect to ground. An observer standing on boat observes that a swimmer S is crossing the river perpendicular to the direction of motion of boat. If river flow velocity is 4 m/s and swimmer crosses the river of width 100 m in 50 sec, then
  1. Drift of swimmer along river is zero
  2. Velocity of swimmer w.r.t ground is 13 m/s
  3. Drift of swimmer along river will be 100 m
  4. Velocity of swimmer w.r.t. ground is 2 ms1


Solution

The correct option is B Velocity of swimmer w.r.t ground is 13 m/s

Here, width of the river =100 m,
Velocity of boat w.r.t ground VBG=3^i m/s (Direction is opposite to +ve  x-axis)
Velocity of river w.r.t ground VRG=4^i m/s
From the boat, the swimmer appears to cross the width of the river (100 m) in 50 seconds perpendicular to the direction of boat (along Y axis).
Hence, VSB=100/50=2^j m/s 
We have,
  VSB=VSGVBG
 VSG=VBG+VSB=3^i+2^j
|VSG|=(32+22) = 13 m/s

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