Question

A man walks in rain with a velocity of 5 km per hour .The rain drops strike at him at an angle of 45 degrees with the horizontal . Velocity of rain if it is falling vertically downward is-

Answer 1

Answer:

From the question we know that the velocity of the man is 5 km/hr and we know that the rain is falling at an angle of 45 degree with the horizon thus the value of tan45 will be velocity of the rain to the velocity of the man.

Hence, the value of tan45 is 1 so, we will get that the velocity of the man is equal to the velocity of the velocity of the rain thus the velocity of the rain will also be 5 km/hr.

Answer 2

Answer:

Velocity of Rain, Vr = 5 km/h

Explanation:

[Refer to the attached image 1 to better understand the case and visualize it]

Given;-

        Velocity of Man, Vm = 5 km/h

        Velocity of rain, Vr = ?

   Angle at which rain falls horizontally, θ= 45°

Now;-

[Refer to attached image 2 to better understand the case and visualize it]

Since,                θ = 45°

Hence,     Vr sinθ = Vr cosθ

Assuming Man to be at rest, then the velocity of man will get added to that of velocity of rain falling but with opposite direction. So, in that case, we obtain;-

                Vm sinθ = Vm

Also, Vm sinθ = Vm cosθ    [since, θ = 45° so, resultant components of v will be equal]

Therefore,   Vm = Vm cosθ = Vm sinθ

And,      ∵ Vm cosθ = Vr

Hence,        Vr = Vm

So,               Vr = 5 km/h

Hence, the velocity of rain if it is falling vertically downwards is 5 km/h.

[Note; Rain man problems are considered harder to understand solve. But, contrary to famous notion of such problems, I very strongly believe that all you need is a certain level of understanding to approach to these problems and then tackle them. So, if your basics are not clear in respect to vector in 2-D motion, firstly clear that out and then approach such cases]

Hope it helps ;-))