Question

two cars are moving in the same direction with a speed of 30 km/h.they are seperated from each other by 5km. third car moving in opposite direction meets the two cars after an interval of 4sec.what is the speed of the third car?

Answer 1

Relative velocity of car A w.r.t. car B is :
V_AB = V_B -V_A = 0
So, relative separation between two cars A and B remains constant at all instants.
If V_C is the velocity of car C w.r.t to ground in the opposite direction to car A and car B, then relative velocity of car C relative to car A or B will be,
V_rel = V_C - (-30) = (V_C + 30 ) km/hr
Time taken by car C to cross cars A and B is
t = d/v_rel = 5/ (​V_C + 30)
4/3600 hr= ​5 km/ (​V_C + 30) km/hr (as 1hr = 3600 s)
on solving we get , velocity of car C, V_C = 4470 km/hr