Question

Melanie and Michael are on the north bank of a river that is flowing east to west at a speed of 0.5 m/s. They paddle their surf ski in the direction S30°E, also at a speed of 0.5 m/s. If the river is 30 metres wide, how long does it take them to cross the river, and how far downstream or upstream are they? Round your answers to one decimal place.

Answer 1

total distance travel by them to cross river is 17.3 m

Explanation:

Assume A be the initial position of both person and B as apposite point to A

u component of velocity along SOUTH DIRECTION is 4 cos30 = 0.4330 m/s

v component of velocity along SOUTH DIRECTION is 4 cos90 = 0 m/s

total speed will be = 0.4330 + 0 = 0.4330 m/s

time taken
`= (width/ of/ river)/(speed)`

time taken
`= (30)/(0.4330) = 69.3 sec`

component of u in downstream direction = 4 cos120 = -0.25 m/s

component of v in downstream direction = 4 cos 0 = 0.5 m/s

total component in downstream will be -0.25 + 0.5 = 0.25

total distance travel by them to cross river is
`= 0.25* 69.3 = 17.3 m`downstream.