Question

A river current has a velocity of 5 km/h relative to the shore. A boat moves in the same direction as the current at 4 km/h relative to the river.

How do you calculate the velocity of the boat relative to the shore?


divide the river’s velocity by the boat’s velocity

subtract the boat’s velocity from the river’s velocity

add the river’s velocity to the boat’s velocity

Answer 1

Correct Answer is

add the river’s velocity to the boat’s velocity

Step-by-step explanation

In this question we have given ,both current and boat are moving in same direction.

let
`V_(C)` be velocity of current

and
`V_(B)` bw velocity of boat

velocity of current with respect to shore
`V_(CS)`=velocity of current -velocity of shore..............(1)

velocity of boat with respect to river,
`V_(BC)`=velocity of boat-velocity of current.........(2)

add equation (1) and equation (2)

velocity of velocity of current with respect to shore+velocity of boat with respect to river =velocity of current(river) -velocity of shore+velocity of boat-velocity of current(river)

`V_(CS)+V_(BS)=V_(C)-V_(s)+V_(B)-V_(C)\\V_(CS)+V_(BS)=V_(S) +V_(B)\\V_(CS)+V_(BS)=V_(BS)`

it means velocity of the boat relative to shore=rivers velocity relative to shore+boat velocity relative to river

velocity of the boat relative to shore=
`4(km)/(h) +5(km)/(h)`

velocity of the boat relative to shore=
`9(km)/(h)`