Question

A boat heads north in still water at 4.5 m/s directly across a river that is running east at 3.0 m/s. What is the velocity of the boat with respect to Earth?

Answer 1

5.41 m/s

Step-by-step explanation:

velocity of boat with respect to water , Vb,w = 4.5 j

velocity of water with respect to ground, Vw,g = 3 i

velocity of boat with respect to water = velocity of boat - velocity of water

Vb,w = Vb, g - Vw, g

4.5 i = Vb,g - 3i

Vb,g = 3 i + 4.5 j

The magnitude of velocity =
`\sqrt{3^(2)+4.5^(2)}` = 5.41 m/s

Answer 2

Velocity of the boat with respect to Earth is 5 m/s 56.31° north of east

Step-by-step explanation:

A boat heads north in still water at 4.5 m/s directly across a river that is running east at 3.0 m/s.

Let north be positive y axis and east be positive x axis.

We have

Velocity of boat = 4.5 j m/s

Velocity of river = 3 i m/s

Velocity of the boat with respect to Earth = 3 i + 4.5 j

`\texttt{Magnitude of velocity = }√(3^2+4.5^2)\\\\\texttt{Magnitude of velocity = }5.41m/s`

`\texttt{Angle = }tan^(-1)\left ( (4.5)/(3)\right )\\\\\texttt{Angle = }56.31^0`

That is 56.31° north of east.

Velocity of the boat with respect to Earth is 5 m/s 56.31° north of east