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?
a) I got .7m/s
b) I got 1stt runner win
c) Idk
To answer these questions, we can use the concept of relative velocity and the formula for calculating the time taken to cover a certain distance at a given velocity. Let's go through each part step by step.
(a) To find the velocity of the second runner relative to the first, we need to subtract the velocity of the first runner from the velocity of the second runner. Therefore, the velocity of the second runner relative to the first is:
Velocity of the second runner relative to first = Velocity of the second runner - Velocity of the first runner
= 4.20 m/s - 3.50 m/s
= 0.70 m/s
So, the velocity of the second runner relative to the first is 0.70 m/s.
(b) To determine who will win the race, we need to consider the time it takes for each runner to cross the finish line.
The time taken by the front runner to cross the finish line can be calculated using the formula:
Time = Distance / Velocity
For the front runner, the distance to the finish line is given as 250 m, and the velocity is 3.50 m/s. Therefore, the time taken by the front runner to cross the finish line is:
Time taken by the front runner = 250 m / 3.50 m/s
= 71.43 s
Similarly, the time taken by the second runner to cross the finish line can be calculated using the same formula:
Time taken by the second runner = 45.0 m / (4.20 m/s - 3.50 m/s)
= 45.0 m / 0.70 m/s
= 64.29 s
Comparing the times taken by both runners, we see that the second runner takes less time to cross the finish line. Therefore, the second runner will win the race assuming they run at constant velocity.
(c) To determine the distance ahead the winner will be when she crosses the finish line, we need to find the difference in distances covered by both runners when the second runner crosses the finish line.
The distance covered by the second runner can be calculated using the formula:
Distance = Velocity x Time
For the second runner, the velocity is 4.20 m/s and the time taken is 64.29 s. Therefore, the distance covered by the second runner before crossing the finish line is:
Distance covered by the second runner = 4.20 m/s x 64.29 s
= 270.01 m
Since the first runner is 250 m from the finish line, the distance the winner will be ahead of the second runner when crossing the finish line is:
Distance ahead the winner = Distance covered by the second runner - Distance to the finish line
= 270.01 m - 250 m
= 20.01 m
Therefore, the winner will be 20.01 meters ahead when she crosses the finish line.