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A man is standing on a road and observes that rain is falling at angle 45 with the vertical. The man starts running on the road with constant acceleration 0.5 m/s2. After a certain time from the start of the motion, it appears to him that rain is still falling at angle 45 with the vertical, with speed 22 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:
  1. It is not possible
  2. Speed of the rain relative to the ground is 2 m/s
  3. Speed of the man when he finds rain to be falling at angle 45 with the vertical, is 4 m/s
  4. The man has travelled a distance 16 m on the road by the time he again finds rain to be falling at angle 45


Solution

The correct options are
C Speed of the man when he finds rain to be falling at angle 45 with the vertical, is 4 m/s
D The man has travelled a distance 16 m on the road by the time he again finds rain to be falling at angle 45
Vrg=Vrm+Vmg


As the man speeds up, the angle with the vertical keeps on decreasing and the rain becomes vertical w.r.t. to the man at some point in time. On increasing the speed further, the angle with the vertical increases on the other side as shown is figure.

Vrm=VrgVmg
Vrmcos45=Vrgcos45
Vrm=22 m/s=Vrg
Vrmcos45=VmgVrgcos45
Vmg=2212+2212=4 m/s
using v2=u2+2as for the motion of man,
v2=u2+2as
or 42=0+2×0.5s
or s=16 m

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