Question

A wildebeest and chicken participate in a race over a 2.00km long course. the wildebeest travels at a speed of 16.0m/s and chicken can do 2.50m/s. the wildebeest runs for 1.600km and then stops to tease the slow-moving chicken, which eventually passes by. the wildebeest waits for a while after the chicken passes and then run toward the finish line. both animal cross the finish line at the exact same instant. assume boat animals, when moving, move steadily at their respective speed.
(a) how far (in m) is the chicken from the Finish Line when the wildebeest resume the race?
(b) for how long in time (in s) was the wildebeest stationary?

Answer 1

Answer:

(a)  The distance of the chicken from the finish line is 62.5 m

(b) The stationary time of the wildebeest is 675 s

Explanation:

Given;

total distance traveled by wildebeest and chicken, d = 2 km = 2000 m

speed of the wildebeest, $v_w$ = 16 m/s

speed of the chicken, $v_c$ = 2.5 m/s

Time for wildebeest to finish the race without stopping, 2000 / 16 = 125 s

Time for chicken to finish the race without stopping, 2000/2.5 = 800 s

(b) for how long in time (in s) was the wildebeest stationary?

t(stationary) = t(chicken) - t(wildebeest)

t = 800s - 125 s

t = 675 s

(a) how far (in m) is the chicken from the Finish Line when the wildebeest resume the race?

The time taken for the wildebeest to run 1.6 km (1600 m) is given by;

t = 1600 / 16 = 100 s

The total time spent by the wildebeest before it resumed the race = stationary time + 100s

t (total) = 675 s + 100 s = 775 s

Distnace traveled by the chicken when the wildebeest resumed the race = 2.5m/s x 775s = 1937.5 m

Thus, the distance of the chicken from the finish line = 2000 m -  1937.5 m

the distance of the chicken from the finish line = 62.5 m