A river 4.0 km wide is flowing at the rate of 2km/hr. The minimum time taken by a boat to cross the river with a speed v=4km/hr (in still water) is approximately

Options

A. 1 hr and 9 minutes
B. 2 hr and 7 minutes
C. 1 hr and 12 minutes
D. 2 hr and 25 minutes

Answer

A

Explanation

Minimum time is taken when the boat crosses the river at right angles to its flow. The resultant velocity of boat and river should be at right angles to flow of river

AD represent resultant velocity `(AC)^(2)=(CD)^(2)+(AD)^(2)implies4^(2)=2^(2)+(AD)^(2)`
`:.R=AD=sqrt(12)`km/h, Width along AD=4km, `:.` Time = Distance /Velocity
`:.4/(sqrt(12))=4/(2sqrt(3))=2/(sqrt(3)0=1.154`hr =69 min =1.hr 9 min