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Question

Two ships are 60 km apart on North-South vertical at an instant as shown in the figure. The one farther North is streaming South at 303 km/hr and the other is streaming East at 30 km/hr. What is the time taken by the ships to reach the closest approach?



Your Answer
A
60 min
Correct Answer
B
52 min
Your Answer
C
30 min
Your Answer
D
45 min

Solution

The correct option is D 52 min
As per the question taking everything in B frame we have
vAB=vAvB
So, we have from above equation
|vAB|=(303)2+(30)2=60 km/hr
and, angle θ is given by
θ=tan1(30303)=tan1(13)=30
Thus, the relative motion can be shown as
So, from the above figure we can say that the relative distance moved by ship A to raech the closest approach is AC, which is given by
AC=60cosθ=60cos3052 km
Hence, time taken by the ships is given by
t=52|vAB|=5260=52 min

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