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Standard XII

Physics

Relative Motion: Rain Example

Raindrops are...

Question

Raindrops are falling vertically with a velocity $10 m / s$ . To a cyclist moving on a straight road the raindrops appear to be coming with a velocity of $20 m / s$ . The velocity of cyclist is

10 m / s

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10 \sqrt{3}

m/s

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20 m / s

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20 \sqrt{3} m / s

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Solution

The correct option is A $10 \sqrt{3}$ m/s
Let the velocity of the cyclist be $v_{x}$
Velocity of the rain is $v_{y} = 10 m / s$
Relative velocity $= - v_{x}$ along $x$ and $v_{y}$ along $y$
Hence relative velocity $= \sqrt{v_{x}^{2} + v_{y}^{2}} = 20 m s^{- 1}$
$v_{x}^{2} + 100 = 400$
$v_{x}^{2} = 400 - 100 = 300$
Therefore, the velocity of cyclist, $v_{x} = 10 \sqrt{3} m s^{- 1}$
Hence option $B$ is correct.

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Raindrops are falling vertically with a velocity 10m/s. To a cyclist moving on a straight road the raindrops appear to be coming with a velocity of 20m/s. The velocity of cyclist is

The correct option is A 10√3 m/sLet the velocity of the cyclist be vxVelocity of the rain is vy=10m/sRelative velocity =−vx along x and vy along yHence relative velocity =√v2x+v2y=20ms−1v2x+100=400v2x=400−100=300Therefore, the velocity of cyclist, vx=10√3ms−1Hence option B is correct.

Raindrops are falling vertically with a velocity $10 m / s$ . To a cyclist moving on a straight road the raindrops appear to be coming with a velocity of $20 m / s$ . The velocity of cyclist is