Question

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 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:It is not possibleSpeed of the rain relative to the ground is 2 m/sSpeed of the man when he finds rain to be falling at angle 45∘ with the vertical, is 4 m/sThe 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=→Vrg−→Vmg Vrmcos45∘=Vrgcos45∘ Vrm=2√2 m/s=Vrg Vrmcos45∘=Vmg−Vrgcos45∘ Vmg=2√21√2+2√21√2=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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