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A man is walking on a level road at a sp...

A man is walking on a level road at a speed of 3.0 km/h. Rain drops fall vertically with a speed of 4.0 km/h. Find the velocity of the raindrops with respect to the man.

Text Solution

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If we consider velocity of rain with respect to the man is `v km//h`.

Relative velocity of man w.r.t. ground `vecv_(mg)=vecv_(m)-vecv_(g) ….(1)` velocity of rain w.r.t. ground `vecv_(rg)=vecv_(r)-vecv_(g) ....(2)`
Velocity of rain w.r.t. man `vecv_(m)=vecv_(r)-vecv_(m)`
On subtracting equaiton (1) form equation (2)
`vecv_(rm)=vecv_(rg)-vecv_(mg)`
`|v_(m)| = sqrt(2_(rg)^(2)+v_(mg)^(2)) = sqrt(4^(2)+3^(2)) = 5km//hr`.
Direction: `tan theta = (3)/(4)` or `theta - tan^(-1) ((3)/(4))`
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