Question

Here's a question, can anyone help me with it ?

​

Answer 1

Question:-

A man standing on a road has to hold his umbrella in 30° with the vertical to keep the rain away.He throws the umbrella and starts running at 10km/h.He finds that raindrops are hitting his head vertically .Find the speed of rain w.r.t road.

Answer:-

Look at the attachment

`\\ \sf\longmapsto tan\Theta=(Perpendicular)/(Base)`

`\\ \sf\longmapsto tan30=(V_(RAIN))/(10)`

`\\ \sf\longmapsto √(3)=(V_(RAIN))/(10)`

`\\ \sf\longmapsto V_(RAIN)=10√(3)km/s`

option C

Answer 2

• From trigonometric ratios:

`{ \boxed{ \rm{ \tan( \theta) = (opposite)/(adjacent) }}} \\`

• theta is 30°

• opposite speed is Vp

• adjacent speed is 10 km/h

`{ \tt{ \tan(30 \degree) = (v _(p) )/(10) }} \\ \\ { \tt{v _(p) = 10 \tan(30 \degree) = 10 * √(3) }} \\ \\ { \underline{ \underline{ \tt{ \: \: v _(p) = 10 √( 3) \: km }}}}`