Average velocity and a runner on a circular track

[D4b34r5]

Homework Statement

A runner times his speed around a circular track with a circumference of 0.520 mi. At the start he is running toward the east and the track starts bending toward the north. If he goes halfway around, he will be running toward the west. He finds that he has run a distance of 0.668 mi in 5.00 min.

(b) What is his average velocity?
_____ m/s at _____° north of east

Homework Equations

V_av=delta r/delta t

The Attempt at a Solution

There was a part A asking for the average speed which I god and it was 3.58m/s but for this one I honestly have no idea. Any help is greatly appreciated!

 

[anathema]

Hello,

To find the average velocity, we can use the formula Vav=delta r/delta t, where delta r is the change in position and delta t is the change in time. In this case, the runner's change in position is 0.668 mi and his change in time is 5.00 min.

Converting 0.668 mi to meters, we get 1075.072 m. Converting 5.00 min to seconds, we get 300 s. Plugging these values into the formula, we get:

Vav = 1075.072 m / 300 s = 3.583 m/s

So, the runner's average velocity is 3.583 m/s. However, we also need to find the direction of this velocity. Since the runner is initially running towards the east and ends up running towards the west, his direction of motion has changed by 180 degrees. This means that his average velocity is directed towards the west, which is 90 degrees north of east.

Therefore, the runner's average velocity is 3.583 m/s at 90 degrees north of east.

I hope this helps! Let me know if you have any further questions.

 

[baba89]

The average velocity of the runner can be calculated by dividing the total distance traveled (0.668 mi) by the total time taken (5.00 min). This gives an average velocity of 0.134 mi/min.

To convert this to meters per second, we can use the conversion factor of 1 mi = 1609.34 m and 1 min = 60 s. Therefore, the average velocity of the runner is 0.134 mi/min x (1609.34 m/1 mi) x (1 min/60 s) = 3.58 m/s.

To determine the direction of the runner's average velocity, we can use the right-hand rule. With the palm of our right hand facing towards the east, our fingers curl in the direction of the runner's motion. This means that the runner's average velocity is towards the north (since the track is bending towards the north).

Therefore, the runner's average velocity is 3.58 m/s at 90° north of east.