Marathon

Two racers are running marathon (42 m) by running 21km in one direction and running back to the place where they started . One racer run with average sped 18 km/h, and the other with speed 14 km/h. How far from the start is second racer when they meet? How much later will second racer come to the finish?

Solution:

v₁=18 km/h
v₂=14 km/h
A... place where slower runner will be when faster runner rich 21 km
B... place of meeting

C... place where direction of running changes

t₁=D/v₁=1,17 h ... time when faster runner rich 21 km
s_A=v₂t₁=16,33 km ... distance which slower runner has pass during time t₁
s_AC=s_AB+s_BC=D-s_A=4,67 km ... path that slower runner has to pass till point C
s_AC=v₁t_x+v₂t_x
where t_x is time which pass till the meeting point B

t_x=s_AC/(v₁+v₂)=0,146 h
s_AB=t_xv₂=2,04 km

Now, distance of the slower runner from the start in the moment of meeting is

s_A+s_AB=2,04 km + 16,33 km =18,37 km

Faster runner need 42km/v₁=2,332 h, while slower runner need 42/v₂=3h to complete the marathon.

So slower runner will rich finish 3h-2,333h=0,67h=40,2 min=2412 sec later

Speed of light

Calculate how much time does light need to arrive from sun to the earth. (c=3x10⁸ m/s, average distnace between sun and earth is d=1,49 x10¹¹ m)

Solution:

t=d/c=500 sec= 8 min 20