A runner times his speed around a circular track with a circumference of 0.508 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 0.678 mi in 4.00 min.

Question

A runner times his speed around a circular track with a circumference of 0.508 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 0.678 mi in 4.00 min.

i need to find average speed in m/s and average velocity in m/s at what direction from north.

Answer 1

average velocity=(velocityfinal -velocityinitial)/2

velocity final= .678/4 *direction of final run

what is the final direction? Well , he has ran .678mi, which is .678/.508 revolutions, or 1 and a third rev, or a final angle of 120 deg. He is sruning at a 90 degree angle to that.

Sketch this out, and if needed, I will critique your thinking. The results will surprise you.

Answer 2

i did not understand it. please solve it till the end

Answer 3

To find the average speed in m/s, we need to convert the distance traveled into meters and the time taken into seconds.

Given:
Distance = 0.678 mi = 0.678 * 1609.34 m (since 1 mi = 1609.34 m)
Time = 4.00 min = 4.00 * 60 s (since 1 min = 60 s)

Average Speed = Distance / Time

Average Speed = (0.678 * 1609.34 m) / (4.00 * 60 s)

Now, we can calculate the average speed.

Average Speed = 1795.8092 m / 240 s
Average Speed ≈ 7.49 m/s

Therefore, the average speed is approximately 7.49 m/s.

To find the average velocity in m/s and the direction from the north, we need to consider both magnitude and direction.

Given:
Magnitude of displacement = 0.678 mi = 0.678 * 1609.34 m
Time = 4.00 min = 4.00 * 60 s

Average Velocity = Displacement / Time

To determine the direction from the north, we can use trigonometry. We know the starting direction is east, the bending of the track is towards the north, and halfway around the track he is running towards the west.

From the given information, we can conclude that the angle from the north will be 90 degrees clockwise.

Now, we can calculate the average velocity and the direction from the north.

Average Velocity = (0.678 * 1609.34 m) / (4.00 * 60 s)

Average Velocity ≈ 119.061 m / 240 s

Average Velocity ≈ 0.496 m/s

Therefore, the average velocity is approximately 0.496 m/s towards the west, which is 90 degrees clockwise from the north.