Question

a boat crosses a 200m wide river at 3m/s ,north relative to water. the river flows at 1 m/s as shown . what is the velocity of the boat as observed on the river back from the boat departed

Answer 1

Answer:
`v_(b)=\hat{i}+3\hat{j}`

Step-by-step explanation:

Given

Width of river
`b=200\ m`

Velocity of boat w.r.t river
`v_(br)=3\ m/s \quad [\text{North}]`

Velocity of river
`v_r=1\ m/s`

Now using relative velocity concept

`v_(br)=v_(b)-v_(r)`

Suppose river is flowing towards east

so
`v_(r)=1\hat{i}`

and
`v_(br)=3\hat{j}`

So

`v_(b)=v_(br)+v_r`

`v_b=3\hat{j}+\hat{i}`

`v_(b)=\hat{i}+3\hat{j}`

So, boat appeared to be moving towards north-east