college physics

One athlete in a race runnng on a long, straight track with a constanct speed v1 is a distance d behind a second athlete running with a constant speed v2.

(a) Under what circumstances is the first athlete able to overtake the second athlete? (Use v_1 for v1, v_2 for v2, and d as appropriate.)

(b) Find the time t it takes the first athlete to overtake the second athlete, in terms of d, v1, and v2.

(c) At what minimum distance d2 from the leading athlete must the finish line be located so that the trailing athlete can at least tie for the first place? Express d2 in terms of d, v1, and v2 by using the result of part (b).

asked by alaa
  1. a.
    Of course, one way for athlete 1 to overtake athlete 2 is for him to accelerate (that is, if v2 > v1).
    But since the given are constant speeds, surely v2 MUST BE LESS THAN v1 in order for athlete 1 to overtake athlete 2, WITHOUT accelerating.

    b.
    Recall that the distance travelled by an object is just speed x time:
    d = vt
    Athlete 2 is ahead by a distance, d, and after some time, t, their distance travelled will be equal (that is, athlete 1 overtakes athlete 2):
    d + (v2)(t) = (v1)(t)
    Solving for t,
    t = d/(v1 - v2)

    c.
    Now there is an additional condition. Athlete 2 is d2 away from the finish line, while athlete 1 is (d + d2) away from the finish line.
    d2 = (v2)t
    from b., we substitute the expression for t:
    d2 = (v2)*(d)/ (v1 - v2)

    Hope this helps~ :3

    posted by Jai

Respond to this Question

First Name

Your Answer

Similar Questions

  1. physics

    One athlete in a race running on a long, straight track with a constant speed v1 is a distance d behind a second athlete running with a constant speed v2. Find the time t it takes the first athlete to overtake the second athlete,
  2. Physics

    An athlete running on curved track with 15 m radius and with speed of 6.7 m/s. If the athlete doesn't tilt to avoid falling down then calculate the torque on the athlete. Assume that the height of the athlete is 1.7 m and center
  3. Physics

    A track athlete runs exactly one complete lap of the track, 400 m circumfrence, in 4.35x10^1 seconds. What is the speed of the athlete , to two significant figures, if they are assumed to run with a constant velocity for the
  4. PHYSICS

    An athlete on a trampoline leaps straight up into the air with an initial speed of 9.3 m/s. Find the following: (b) the speed of the athlete when she is halfway up to her maximum height
  5. Physics

    An athlete use his last 0.9s to jump from 40m to another position of 44m of a race.Find the linear acceleration of the athlete if it is assumed to be constant
  6. algebra

    Heart Rate An athlete starts running and continues for 10 seconds. The polynomial calculates the heart rate of the athlete in beats per minute t seconds after beginning the run, where . (a) What is the athlete’s heart rate when
  7. Physical science

    Athlete runs twice round the circular athletics track. The track has a total length of 320 m and a diameter of 100 m. Make a scale drawing of the track. Use a scale of 1 cm represents 10 m. Taking the start as point 1, find both
  8. Physics

    A track athlete runs exactly one complete lap of the track, 400 m circumfrence, in 4.02x10^1 seconds. What is the velocity of the athlete , to two significant figures, if they are assumed to run with a constant velocity for the
  9. Physics

    An athlete competing in long jump leaves the ground with a speed of 9.14 m/s at an angle of 35 degrees above the horizontal. What is the length of the athlete's jump?
  10. physics

    An athlete runs from one end to the other end of a semicircular track whose radius is 70m. What is the total distance covered by the athlete and what is his displacement?

More Similar Questions