Suppose a boat moves at 12.0 m/s relative to the water. If the boat is in a river with the current directed east at 2.50 m/s, what is the boat's speed relative to the ground when it is heading (a) east, with the current, and (b) west, against the current?

(a) 14.5 m / s

(b) 9.5 m / s

Explanation:

(a) velocity of boat with respect to water

V (b, w) = 12 i m/s

Velocity of water with respect to ground

V (w, g) = 2.5 i m/s

By the formula of relative velocity

Velocity of boat with respect to ground

V (b, g) = V (b, w) + V (w, g)

V (b, g) = 12 i = 2.5 i = 14.5 i m/s

Magnitude of velocity of boat with respect to ground = 14.5 m/s along + X axis.

(b) velocity of boat with respect to water

V (b, w) = - 12 i m/s

Velocity of water with respect to ground

V (w, g) = 2.5 i m/s

By the formula of relative velocity

Velocity of boat with respect to ground

V (b, g) = V (b, w) + V (w, g)

V (b, g) = - 12 i = 2.5 i = - 9.5 i m/s

Magnitude of velocity of boat with respect to ground = 9.5 m/s along - X axis.