Addition of Velocities

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 3.45 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? (Enter a number. Enter your answer in m/s faster than the front runner.)

___ m/s faster than the front runner

(b)

If the front runner is 250 m from the finish line, who will win the race, assuming they run at constant velocity?

___The second runner will win.

___The first runner will win.    

(c)

What distance (in m) ahead will the winner be when she crosses the finish line? (Enter a number.)

 ___m

Answer 1

(a) let's assume positive direction to right. Then first runner has velocity + 4.20, second + 3.45, relative velocity of second relative to first = (+3.45) - (4.20) = -0.75 m/s (so every second the second runner gets 0.75 m further behind the first).

(b) Obviously the first will win (as the relative velocity of the second to the first is negative the second will get further behind the first as time moves forward so can't catch the first up at any time)

(c) At time zero second runner is at (0,0) and first is at (45,0). The finish line is at (45 + 250,0) = (295,0).

It will take the first runner 250 / 4.20 seconds to get there, at that point position of second runner is

( 0 + (250/4.20) x 3.45, 0). So winner will be (295 - (250/4.20) x 3.45) ) m ahead