A child in danger of drowing in a river is being carried downstream by a current that flows uniformly at a speed of 
m/sec. The child is 600m from shore and 800m downstream of a helipad when the rescue helicopter sets out and the helicopter follows the same direction throughout the motion. If the helicopter proceeds at its maximum speed of 
m/sec. with respect to air and air is blowing with velocity of 4m/sec perpendicular to river flow velocity as shown, then
(i) Heading at what angle with the shore should the helicopter take off?
(ii) calculate the time taken by helicopter to reach the child.
Text Solution
Verified by ExpertsCHECK THE SOLUTION
(i) 37º
(ii) 50 sec
Sol. Velocity of helicopter and child is as shown
Now velocity of helicopter with respect to child
tan φ = 
= 
⇒ tan θ = 
⇒ θ = 37º
Now horizontal velocity = 
= 
= 16 m/s
So time taken = 
= 50 sec.
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