A relay race is run along a straight line track 300.0 m long running south to north. 1st runner - starts at the South end of the track and passes the baton to a teammate at the north end of the track. 2nd runner - races back to the start line and passes the baton to a 3rd runner who races 100.0 m north to the finish line. The magnitude of the average velocities of the 1st, 2nd, and 3rd runners during their parts of the race are 7.30 m/s, 7.20 m/s, and 7.80 m/s. What is the average velocity of the baton for the entire race?

What you DON'T do is average the three velocities. The number you gat will be close (in this case), but it won't be correct.

The total distance run is 300 x 3 = 900 m

The times required by the runners are
300/7.3, 300/7.2 and 300/7.8 s. That is 41.10, 41.67 and 38.46 s. The total time is 121.23s. Divide the total distance by that total time to get the everage speed.

I get about 7.424 m/s

The average of the three speeds is 7.433 m/s

To find the average velocity of the baton for the entire race, we need to calculate the total displacement of the baton and divide it by the time taken for the entire race.

Let's first calculate the displacement of each runner:

1st runner: The magnitude of the average velocity of the 1st runner is given as 7.30 m/s. Since the runner starts at the South end and passes the baton to the next runner at the North end, the displacement is 300.0 m (the length of the track).

2nd runner: The magnitude of the average velocity of the 2nd runner is given as 7.20 m/s. The runner races back to the start line, so the displacement is -300.0 m (negative sign indicates moving in the opposite direction).

3rd runner: The magnitude of the average velocity of the 3rd runner is given as 7.80 m/s. The runner races 100.0 m north to the finish line, so the displacement is 100.0 m.

Now, let's calculate the time taken for each runner:

The distance covered by each runner can be found by dividing the displacement by the magnitude of the average velocity.

1st runner: Time taken = Displacement / Average velocity = 300.0 m / 7.30 m/s = 41.10 s

2nd runner: Time taken = Displacement / Average velocity = (-300.0 m) / 7.20 m/s = -41.67 s (negative sign indicates moving in the opposite direction)

3rd runner: Time taken = Displacement / Average velocity = 100.0 m / 7.80 m/s = 12.82 s

To calculate the total displacement of the baton, we can add up the displacements of the individual runners:

Total Displacement = Displacement of 1st runner + Displacement of 2nd runner + Displacement of 3rd runner
= 300.0 m + (-300.0 m) + 100.0 m
= 100.0 m

To calculate the total time taken for the entire race, we can add up the times taken by each runner:

Total Time = Time taken by 1st runner + Time taken by 2nd runner + Time taken by 3rd runner
= 41.10 s + (-41.67 s) + 12.82 s
= 12.25 s

Finally, we can calculate the average velocity of the baton for the entire race:

Average Velocity = Total Displacement / Total Time
= 100.0 m / 12.25 s
≈ 8.16 m/s

Therefore, the average velocity of the baton for the entire race is approximately 8.16 m/s.