Question

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?

Answer 1

(a) 14.5 m /s

(b) 9.5 m /s

Step-by-step 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.