Question

A boat is traveling upstream at 10 km/h with respect to the water of a river. The water is flowing at 8.0 km/h with respect to the ground. What are the (a) magnitude and (b) direction of the boat’s velocity with respect to the ground? A child on the boat walks from front to rear at 4.0 km/h with respect to the boat.What are the (c) magnitude and (d) direction of the child’s velocity with respect to the ground?

Answer 1

(A). The magnitude and direction of the boat's velocity with respect to the ground is 2 km/h in positive x-axis.

(B). The magnitude and direction of the child’s velocity with respect to the ground is 2 km/h in negative x-axis.

Step-by-step explanation:

Given that,

The velocity of the boat
`v_(bw)= 10\ km/h`

The velocity of the water
`v_(wG) = 8.0\ km/h`

(a). We need to calculate the magnitude of the boat's velocity with respect to the ground.

The equation for the the boat's velocity with respect to the ground

`v_(bG)=v_(bw)-v_(wG)`

`v_(bG)=10-8=2\ km/h`

(b). The direction of the boat's velocity with respect to the ground is in positive x axis.

(c). The velocity of the child with respect to the boat

`v_(cb)=4.0\ km/h`

The magnitude of the child’s velocity with respect to the ground can be found,

`v_(cG)=-\vec{V_(cb)}+\vec{v_(bG)}`

`v_(cG)=-4i+2i`

`v_(cG)=-2i\ km/h`

The magnitude of the child’s velocity with respect to the ground is

`v_(cG)=|\vec{v_(cG)}|=-2\ km/h`

(d). The direction of the child’s velocity with respect to the ground is in negative x-axis.

Hence, (A). The magnitude and direction of the boat's velocity with respect to the ground is 2 km/h in positive x-axis.

(B). The magnitude and direction of the child’s velocity with respect to the ground is 2 km/h in negative x-axis.