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 th

Question

3 years ago

8

e boat with respect to Earth?

2 answers:

Fynjy0 [20] · Answer 1 · 2022-03-27T05:27:15+03:00

<h2>Velocity of the boat with respect to Earth is 5 m/s 56.31° north of east</h2>

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

$\texttt{Magnitude of velocity = }\sqrt{3^2+4.5^2}\\\\\texttt{Magnitude of velocity = }5.41m/s$

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

That is 56.31° north of east.

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

Ilya [14] · Answer 2 · 2022-03-27T07:49:38+03:00

Answer:

5.41 m/s

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