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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

  • If sec theta + tan theta = x,then tan theta is

    A
    `((x^2+1))/x`
    B
    `((x^2-1))/x`
    C
    `((x^2+1))/(2x)`
    D
    `((x^2-1))/(2x)`

  • (sec theta + tan theta) (1- sin theta) =

    A
    `cos theta`
    B
    `cos^2 theta`
    C
    `sin^2 theta`
    D
    `tan^2 theta`

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