Question

A man is running on a horizontal road at 3m/s (along positive x direction ) find that rain is falling vertically. He increase his speed to theta m/s and find that rain drops make angle 30 degree with vertical velocity of rain w.r t. road is (positive y is along vertically upward)???? anybody help me in this question NO SPAM PLEASE​

Answer 1

Solution:-Let the velocity of rain with respect to the road be

$ui \: + vj$

Since the man is observing only vertical velocity of rain,it means it's horizontal velocity is same as the velocity of horizontal component of the rain..

hence

u=3m/s

Velocity of rain with respect to the man=

$3i + vj - 3i = vj$

now ,when he increase his speed upto ∅

then,

velocity of rain with respect to man=

$3i + vj - (3+ theta)i = - thetai \: + vj$

this makes an angle 30° with vertical

as we know

$tan30 = \frac{horizontal \: componenet}{vertical \: component} \\ \frac{1}{ \sqrt{3} } = \frac{theta}{v} \\ v = theta\sqrt{3} \\ also \: we \: know \: u = 3$

so, velocity of rain with respect to road=

$3i + theta\sqrt{3}j \\ their \: magnitude = \sqrt{ {3}^{2} + {(theta \sqrt{3} })^{2}} \\ magnitude \: of \: velocity = \sqrt{9 + 3 {theta}^{2} }$

{hope it helps you}