Since the plane is traveling NE, we know that it is traveling at an angle of 45 degrees north of east. Therefore, we can represent this in a diagram:

We have all of the information we need to solve for the velocity of the plane. We have an angle and a side adjacent to that angle. Therefore, we can use the cosine function to solve for the velocity.

Rearranging for v, we get:

If the car is traveling NW, it means that the angle  is  degrees above the x-axis. Using this angle, and the fact that the magnitude of the velocity is  mph, we can find the x and y components, or the west and north components using trigonometry.

Write the formula for the linear velocity.

The diameter is twice the radius.

If the diameter was decreased by one half, the radius will also decrease by one half.

Therefore:

The linear velocity will decrease by one half.

Write the linear velocity formula.

Since the answer is required in meters per second, two conversions will need to be made.

Convert 30 kilometers to meters.

Convert 2 hours to seconds.

Apply the formula.

Linear velocity is defined as distance over a period of time. For instance if a person ran 1 mile or approximately 1600 meters in 7 minutes, the they would have covered about 230 meters per minute. Let's assume this person was running around a track. We could also measure their speed from a central angle and represent their speed as the amount of degrees (or radians) they ran around per unit time as well. This is considered angular speed. A perfect example of both are the hands on a clock. There is a relationship between arc length which we designate s, the radius r, and the angle  (theta). The relationship is . So the length of the arc (s) is equal to the radius of the circle the arc is on and what section of the pie it covers ( this is akin to how many degrees our track runner ran "through" or around) . Thus, if we wanted the linear speed around a circle we could say  or . Key measurements that you will need to know are how many degrees in a circle of which there are 360 or . Before you follow the step by step solution below, go back and see if you can use this new information to arrive at the correct answer.

The actual answer is .

To see why, note that the second hand spins around a total of 360 degrees or .

.

And how long does it take for the hand to go around? Linear speed of the clock second hand is 

  (rounded answer).

Linear speed is equal to the arc length traversed divided by the time. We use s to denote arc length.

Write the conversion factor between radians and degrees.

Cancel the radians unit by using dimensional analysis.

Write the conversion factor of radians and degrees.

Substitute the degree measure into .

Firstly, since the point  is in the 3rd quadrant, it'll be between  and . If we take  to be the horizontal, we can form a triangle with base and leg of values  and . Solving for the angle in the 3rd quadrant given by , 

Since this angle is made by assuming  to be the horizontal, the total angle measure  is going to be:

In order to solve for the degree measure from radians, replace the  radians with 180 degrees.  

The nearest degree is .