Question

Use appropriate units and significant figures.  USE THE LAW OF COSINES AND LAW OF SINES.

You are flying 75.0 mi/hr on a plane heading north with a wind blowing 15.0 mi/hr 46.0° East of North. What is the resultant velocity (your velocity relative to the ground)?​

Answer 1

The resultant velocity is 86.1 mi/h.

Step-by-step explanation:

The law of cosines is given by:

`c^(2) = a^(2) + b^(2) - 2abcos(\theta)`

Where:

c: is the resultant velocity =?

a: is the velocity of the plane = 75.0 mi/h

b: is the velocity of the wind = 15.0 mi/h

θ: is the angle between "a" and "b"

The angle between "a" and "b" can be found as follows:

`\theta = 180.0 - 46.0 = 134.0 ^(\circ)`

Now, by using the law of cosines we have:

`c^(2) = (75.0)^(2) + (15.0)^(2) - 2*75.0*15.0*cos(134.0) = 7413.0`

`c = 86.1 mi/h`

Therefore, the resultant velocity is 86.1 mi/h.

The law of sines is:

`(a)/(sin(\gamma)) = (b)/(sin(\alpha)) = (c)/(sin(\theta))`

Where:

γ: is the angle between "b" and "c"

α: is the angle between "a" and "c"

So, if we want to find "c" by using the law of sines, we need to know another angle besides θ (γ or α), and the statement does not give us.

I hope it helps you!