Question

You drive 30 miles due east in a half hour. Then, you turn left and drive 30 miles north in 1 hour. What are your average speed and velocity, and what are the rectangular and polar coordinates of your position?

Answer 1

Answer: Your speed is 40 mph. The coordinates are (30, 30) or (42.43 miles, 45 degrees).

First, is the speed. We traveled a total of 60 miles in 1.5 hours. Dividing that gives us an average speed of 40 miles per hour.

Second, the first set of coordinates is just (30, 30) because it is 30 the right and 30 up. 

Third, the polar coordinates are (42.43 miles, 45 degrees). We can use the Pythagorean Theorem to find the first part. And we know the second part is 45 degrees because it is an isosceles right triangle.