A river flows 3 kmh -1 and a man is capable of swimming 2 km h -1 . He wishes to cross it in minimum time. In which direction will he swim?
Text Solution
Verified by ExpertsThe correct answer is:
A
Let us assume he swims at an angle θ θ with the perpendicular as shown. If river is lm wide time taken to cross it
t = l/2cos θ θ , v x = 3 – 2 sin θ θ horizontal distance covered along x direction during this period x = v x .
t = (3 – 2 sin θ θ ) l/2cos θ θ
for t to be min dx/d θ θ = 0, or
l[3/2 sec θ θ tan θ θ - sec 2 θ θ ] = 0 or
sin θ θ = 2/3
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