Question

Near the end of a marathon race, the first two runners are separated by a distance of 45.0 m. The front runner has a velocity of 3.50 m/s, and the second a velocity of 4.20 m/s.

(a) What is the velocity of the second runner relative to the first?
(b) If the front runner is 250 m from the finish line, who will win the race, assuming they run at constant velocity?
(c) What distance ahead will the winner be when she crosses the finish line?

The velocity of the second runner relative to the first is approximately:

a) 0.70 m/s
b) 0.80 m/s
c) 0.90 m/s
d) 1.00 m/s

Answer 1

The velocity of the second runner relative to the first is 0.70 m/s. Assuming constant velocity, the front runner will win the race. The winner will be 295 m ahead of the second runner when she crosses the finish line.

Step-by-step explanation:

(a) To find the velocity of the second runner relative to the first, we subtract the velocity of the first runner from the velocity of the second runner:

Velocity of the second runner relative to the first = Velocity of the second runner - Velocity of the first runner

Velocity of the second runner relative to the first = 4.20 m/s - 3.50 m/s = 0.70 m/s

(b) To determine who will win the race, we need to compare the distances each runner needs to cover to reach the finish line.

The front runner is 250 m from the finish line, while the second runner is 45.0 m behind the front runner.

Since the front runner has a shorter distance to cover, assuming they run at constant velocity, the front runner will win the race.

(c) When the winner crosses the finish line, she will have covered a total distance of 250 m.

Since the second runner is 45.0 m behind the front runner, the winner will be 295 m ahead of the second runner when she crosses the finish line.