Question

A 140 m wide river flows due east at a uniform speed. If a boat heads directly north across the river with a velocity of 5 m/s, what is the boat's resultant velocity relative to the river bank?

Options:
a) 5 m/s
b) 7 m/s
c) 9 m/s
d) 10 m/s
e) 12 m/s

Answer 1

The boat's resultant velocity relative to the river bank is 5 m/s.

Step-by-step explanation:

To find the boat's resultant velocity relative to the river bank, we can use the concept of vector addition. The boat's velocity relative to the river bank can be found by adding the velocity of the boat relative to the river to the velocity of the river. This can be represented graphically by drawing vectors to scale and adding them using the triangle rule or using trigonometric functions.

Given that the boat's velocity relative to the river is 5 m/s north and the velocity of the river is due east, we can see that these velocities are perpendicular to each other. Therefore, we can use the Pythagorean theorem to find the magnitude of the resultant velocity:

Resultant velocity = sqrt((velocity of the boat)^2 + (velocity of the river)^2)

Substituting the given values, we get:

Resultant velocity = sqrt((5 m/s)^2 + (0 m/s)^2) = 5 m/s

So, the boat's resultant velocity relative to the river bank is 5 m/s.