A man is standing on a road and observes that rain is falling at angle 45º with the vertical. The man starts running on the road with constant acceleration 0.5 m/s 2 . After a certain time from the start of the motion, it appears to him that rain is still falling at angle 45 º with the vertical, with speed 2√2 m/s . Motion of the man is in the same vertical plane in which the rain is falling. Then which of the following statement(s) are true.
| (A) | It is not possible |
| (B) | Speed of the rain relative to the ground is 2 m/s. |
| (C) | Speed of the man when he finds rain to be falling at angle 45º with the vertical, is 4m/s. |
| (D) | The man has travelled a distance 16m on the road by the time he again finds rain to be falling at angle 45°. there can be more than one option correct |
Ans. C. and D.
The case is possible if the following diagram is considered.
When the man is standing stationary w.r.t ground then, rain falls as in figure 1. And when he accelerates he sees as in fig. 2
Let the rain fall with a velocity v w.r.t ground. Let the man have a speed u when he sees the rain falling down with angle 45o with the vertical.
Angle between v and u is θ = 3×45o = 135o
Now angle made by resultant RO with v is β = 90o
