Question

A hunter wishes to cross a river that is 1.5 km wide and flows with a velocity of 5.0 km/h parallel to its banks. The hunter uses a small powerboat that moves at a maximum speed of 12 km/h with respect to the water. What is the minimum time for crossing?

Answer 1

Answer:137.48 s

Step-by-step explanation:

Given

Width of river=1.5 km

velocity of river=5 km/h

velocity of boat w.r.t river =12 km/h

To cross the river in minimum time hunter needs to cross the river perpendicular to the flow

i.e. velocity of boat w.r.t water must be perpendicular

i.e. x component of boat must be equal to river flow

`12cos\theta =5`

where
`\theta` is angle made by boat w.r.t bank

`cos\theta =(5)/(12)`

`cos\theta =0.416`

`\theta =65.417^(\circ)`

its vertical component is
`12sin(65.417)=10.91 m/s`

Time taken
`=(1.5* 1000)/(10.91)=137.48 s`