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

Answer:

(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.

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.