A man of mass `M = 58 kg` jumps from an airplane as shown in Fig. He sees the hard ground below him and a lake at a distance `d = 1 m` from the point directly below him. He immediately puts off his jacket (mass `m = 2` kg) and throws it in a direction directly away from the lake. If he just fails to strike the ground, find the distance (in `10^(1) m`) he should walk now to pick his jacket. (Neglect air resistance and take the velocity of man at the time of jump with respect to earth zero.)

Answer

3

Explanation

To save himself, the man throws his jacket in opposite direction to the lake. According to momentum conservation, he himself gets a velocity in the direction of the lake. During the motion as gravity is the only external force on the system (man plus jacket), centre of mass will not be displaced horizontally. Thus, centre of mass of the system falls vertically andn when the man falls in the lake, jacket falls at a point such that the centre of mass of the man and the jacket will be directly below the point from where the man jumps).
As it is given that man falls at a distance `d` from this point, it implies that jacket will fall at a distance `x` in the, opposite directionn such that
`mx=Mdimpliesm=M/md=29m`,
mann has to travel a distance `x=d=29+1=30m` to pick his jacket.