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?

Question

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?

drwls · Answer

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