Question

A boat that moves with a constant velocity of 12 m/s is moving on a river with a
constant current of 4 m/s. What is the resultant velocity of the boat if:
a) The boat is traveling to the north and the current is to the south?
b) The boat is traveling to the south and the current is to the south?
c) The boat travels to the east, across the current, while the current is to the south.

Answer 1

Explanation:

Given that,

Velocity of boat, $v_b=12\ m/s$

Velocity of current, $v_c=4\ m/s$

(a) If the boat is traveling to the north and the current is to the south,

$v_b=12j\ m/s$

$v_c=-4j\ m/s$

The resultant velocity,

$v_r=12-(4)=8\ m/s$ due North

(b) If boat is traveling to the south and the current is to the south,

$v_b=-12j\ m/s$

$v_c=-4j\ m/s$

Resultant velocity,

$v_r=12+4=16\ m/s$ due south

(c) If the boat travels to the east, across the current, while the current is to the south.

So,

$v_r=\sqrt{12^2+4^2}\\ \\v_r=12.64\ m/s$