Question

Two children who are bored while waiting for their flight at the airport decide to race from one end of the 20-m-long moving sidewalk to the other and back. Phillippe runs on the sidewalk at 2.0 m/s (relative to the sidewalk). Renee runs on the floor at 2.0 m/s. The sidewalk moves at 1.5 m/s relative to the floor. Both make the turn instantly with no loss of speed. a. Who wins the race

Answer 1

Answer: Phillipe wins the race

Explanation:

Given

Length of track=20 m

Velocity of Phillippe=2 m/s w.r.t sidewalk

Velocity of sidewalk=1.5 m/s

Rena velocity=2 m/s

Therefore absolute velocity of P is 2+1.5=3.5 m/s

Time taken by phillippe $\frac{20}{3.5}+\frac{20}{3.5-1.5}$

$t_P$=5.714+10=15.714 s

Time taken by rena

$t_r=\frac{20}{2}+\frac{20}{2}=20 s$

as the time taken  by phillippe is less than rena therefore Phillippe wins the race.

Answer 2

Answer:

Renee will win the race

Explanation:

Total time of motion for Phillippe is given as

$t_1 = \frac{L}{v + v_1 } + \frac{L}{v - v_1}$

now we have

$t_1 = \frac{L}{2 + 1.5} + \frac{L}{2 - 1.5}$

$t_1 = \frac{L}{3.5} + \frac{L}{0.5}$

$t_1 = 2.28 L$

now for Renee we have

$t_2 = \frac{L}{2} + \frac{L}{2}$

$t_2 = L$

so here we can see that

$t_2 < t_1$

so Renee will win the race