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

- Drift of swimmer along river is zero
- Velocity of swimmer w.r.t ground is √13 m/s
- Drift of swimmer along river will be 100 m
- Velocity of swimmer w.r.t. ground is 2 ms−1

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=−−→VSG−−−→VBG

⇒ −−→VSG=−−→VBG+−−→VSB=−3^i+2^j

|−−→VSG|=√(32+22) = √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=−−→VSG−−−→VBG

⇒ −−→VSG=−−→VBG+−−→VSB=−3^i+2^j

|−−→VSG|=√(32+22) = √13 m/s

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