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Question

Two swimmers swim in a stand still lake. First swimmer swims directly across the lake (30 m wide) with a velocity of 1.5 m/s, reaches the other end and runs a distance of 10 m in 10 seconds along the shore. What should be the velocity of the second swimmer so that he reaches the same point in the same time ?
  1. (13^i+^j) m/s
  2. (1^i1.5^j) m/s
  3. (1.5^i1^j) m/s
  4. (1.5^i+1^j) m/s


Solution

The correct option is A (13^i+^j) m/s

Velocity of first swimmer, v1=1.5 m/s 
Time taken to cover 10 m along the shore, tQR=10 s
For the second swimmer to reach the same point in same time, he should cover equal displacement in equal time.
Displacement of first swimmer, S=10^i+30^j
Time taken by first swimmer to reach the point R, t=tPQ+tQR
t=301.5+10=30 s
Therefore , velocity of second swimmer, v2=St=10^i+30^j30=(13^i+^j) m/s

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