Question

A boat is traveling upstream at 11 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 5.0 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

Solution :

Given :

V_{boat wrt water} = 11 km/h

V_{water wrt ground} = - 8 km/h

V_{child wrt boat} = - 5 km/h

(a) magnitude of the boat’s velocity with respect to the ground :

V_{boat wrt ground} = V_{boat wrt water} + V_{water wrt ground} = 11 km/h + (-8 km/h) = 3 km/h

(b) direction of the boat’s velocity with respect to the ground is Positive. (same as the direction of boat wrt to water)

A child on the boat walks from front to rear at 5.0 km/h with respect to the boat.What are the -

(c) magnitude of the child’s velocity with respect to the ground :

V_{child wrt ground =} V_{child wrt boat +} V_{boat wrt ground} = (-5 km/h) + 3 km/h  = -2 km/h

Thus :  magnitude of the child’s velocity with respect to the ground is 2 km/h.

(d) direction of the child’s velocity with respect to the ground is Negative.