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The speed of the particle at time= 6 sec
Suppose that two objects A and B are moving with velocities (each with respect to some common frame of reference). Letrepresent the velocity of A with respect to B. Then
Velocity of object A relative to that of B is
Velocity of object B relative to that of A is
Rain is falling vertically with a speed of 30 ms−1. A woman rides a bicycle with a speed of 12 ms−1 in east to west direction. In which direction she should hold her umbrella?
In the figure, represents the velocity of rain and vb the velocity of the bicycle, the woman is riding. To protect herself from rain, the woman should hold her umbrella in the direction of the relative velocity of rain with respect to the bicycleFrom figure,
Therefore, the woman should hold her umbrella at an angle of tan−1(2/5)with the vertical towards the west.
A river is flowing from west to east with a speed 5 ms−1. A swimmer can swim in still water at a speed of 10 ms−1. If he wants to start from point A on south bank and reach opposite point B on north bank, in what direction should he swim?
Here, Velocity of swimmer in still water, vs = 10ms−1
Velocity of water flowing in river, vr = 5ms−1
From figure, sinθ = vr/vs = 5/10 = 1/2
θ = sin−1(.1/2) = 30∘ west of north
A girl riding a bicycle with a speed of 5 ms−1 towards north direction, observes rain falling vertically down. If she increases her speed to 10 ms−1, rain appears to meet her at 45∘ to the vertical. What is the speed of the rain?