Answer:
a. 0.7 m/s
b. The second runner
c. 4.20 meters
Explanation:
a. To know the relative speed we can use the following equation:
Relative Speed (Vr) = V1 - V2
The relative speed is used to compared the velocity of one object (V1) to another object (V2). To learn the Relative Velocity from the second runner to the first we do the following:
Relative Speed (Vr) = Second Runner Velocity (Vs) - First Runner Velocity (Vf)
Vr = 4.20 m/s - 3.50 m/s
Vr = 0.7 m/s
This means that the second runner is gaining 0.7 meter from the first runner each second.
b. To know which runner will gain the race, we need to keep in mind, that the seconds runner is 45 meter more away that the first runner from the goal. Knowing this, the winner will be the one that reach the goal on less time.
Because movement is constant, we can use the following equation:
Velocity (V) = Distance (D) / Time (T)
To get the time we do:
T = D / V
Now, for the first runner:
T = 250 meters / (3.50 m/s)
T = 71.42 seconds
For the second runner.
T = (250 meters + 45 meters) / (4.20 m/s)
T = 70,23 seconds
Because the second runner takes less time to reach the goal, he wins the race.
c. Because it is know how much time takes the winner to get to the finish line, we can use that same time to know how far was the first runner from the goal. This is posible we know that how far he is from the goal is as follows.
Distance from goal (Dg) = Total Distance (D) - Distance travelled (Dt)
Where Total Distance (D) is 250 mts. And the distance travelled can be obtained by using the following equation.
Velocity (V) = Distance (D) / Time (T)
Searching for distance:
D = V / T.
D = (3.50 m/s) * 70.23 s
D = 245,80 meters
Soo
Distance from goal (Dg) = Total Distance (D) - Distance travelled (Dt)
Dg = 250 meters - 245,80 meters
Dg = 4,20 meters
The first runner was 4,20 meter behind the second one when the second runner crossed the goal
