Who wins the race? By how much time?

Question

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

 

A) Who wins the race?

 

B) By how much time does the winner win?

Answer 1

 

 

*start here                                         * turn here

 

_________________________________V  = 2.0 mls (Phillipe)   ------->

 

----------------------------------------------Vo = 1.5 m/s (sidewalk)------->

 

*********************************U = 2.0 m/s (Renee)     ------->

 

For the first leg

t1(Renee) = 20.0m/2.0m/s = 10 seconds

 

V1(Phillipe) = 2.0m/s + 1.5 m/s =3.5m/s

t1(Phillipe) = 20.0m/3.5m/s = 5.71 seconds

 

__________________________________ V  = 2.0 m/s (Phillipe)  <--------

 

------------------------------------------------ Vo= 1.5 m/s (sidewalk)  ------->

 

***********************************U = 2.0 m/s (Renee)     <--------

 

For return trip, the time Renee's time is the same as before

t2(Renee) = 10 second

 

V2(Phillipe) = 2.0m/s - 1.5 m/s = 0.5 m/s

t2 (Phillipe) = 20.0 m/0.5 m/s = 40 seconds

 

Renee took = 10sec + 10sec = 20 seconds

Phillipe took = 5.71 sec + 40 sec = 45.71 seconds

 

(a) Renee wins the race

(b) Difference in time taken between Phillipe and Renee is = 45.71 - 20 = 25.71 seconds