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A man walking briskly in rain with speed...

A man walking briskly in rain with speed v must slant his umbrella forward making an angle `theta` with the vertical. A student derives the following relation between `theta` and v: `tan theta` = v and checks that the relation has a correct limit : as `vtoo, thetato0`, as expected , (we are assuming there is no strong wind and that the rain falls vertically for a stationary man.) Do you think this relation can be correct ? If you, guess the correct relation.

Text Solution

Verified by Experts

tan `theta` must be dimensionless . The correct formula is tan`theta = v//v.` where v. is the speed of rainfall.
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Knowledge Check

  • The relation between B_(h), B_(v) and B is ……..

    A
    `B= sqrt(B_(h)^(2)+B_(v)^(2))`
    B
    `B= B_(h).B_(v)`
    C
    `B= (B_(v))/(B_(h))`
    D
    `B= (B_(h))/(B_(v))`

  • The relation between B_(v) , B_(h) and B is ….... .

    A
    `B= sqrt(B_(h)^(2) + B_(v)^(2))`
    B
    `B= B_(h). B_(v)`
    C
    `B= (B_v)/( B_h)`
    D
    `B= (B_h)/(B_v)`

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