Question

A river 4.0 miles wide is following at the rate of 2 miles/hr. The minimum time taken by a boat to cross the river with a speed v=4 miles/hr (in still water) is approximately
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 1

Correct Answer - A
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 or river.
AD represent resultant velocity (R) By right angled tirangle,
`(AC)^(2)=(CD)^(2)+(AD)^(2)`
`(4)^(2)=(2)^(2)^(2)+(AD)^(2)`
or `R=AD=sqrt(12)mph`
Width along AD=4 miles
`therefore "Time"=("Distance")/("velocity")=(4)sqrt(12)=(4)/(2sqrt(3))=(2)/(1.732)`
`=1.154h`
`therefore "Time"=1` hour 9 min.