A motor boat moving downstream overcame a raft at a point A; after τ (Tau) min, it turned back and after some time, met the raft again at a distance l = 6 km from point A. Calculate flow of velocity assuming the speed of the boat is constant.
- Question
- NEET
- Motion in a Straight line
- Relative Velocity in 1D
- 11th
Step-wise Solution :
Problem Logic decode
A motorboat and river both moves with a constant velocity. There is a raft, a wooden plank floats over river, moves along with the river flow downstream (motion of body along the river flow). So, if a boat moves downstream, net velocity of boat with respect to ground will be actual velocity of boat plus the velocity of river, since both acts in the same direction. If the boat moves upstream (motion of body opposite to river flow), river velocity tries to balance the boat velocity, thus net velocity of boat with respect to ground decreases. Given that, boat completes the downstream journey in 1 hour and takes other ‘t’ hours to meet the raft again in upstream journey. When the motorboat meets the raft, the time taken will be (1+t) hours, where the net displacement for both the raft as well as motorboat is +6 km (downstream).
To find the flow velocity, use the displacement relation of raft and motorboat. Form the equations for the displacement under the assumption that river moves with constant velocity and boat moves with constant velocity in both downstream and upstream.