Answer to Question #238914 in Mechanics | Relativity for Omar Q.

Question

Two cars are driving toward each other on a straight and level road. One car is traveling at 100 km/h north and the other car is traveling at 42.0 km/h south, both velocities measured relative to the road. At a certain instant, the distance between the cars is 10.0 km. How long will take for the two cars to meet?

Answer 1

The distance traveled by the first car $x=v_1 \times t$

The distance traveled by the second car $d-x = v_2 \times t$

$v_1 \times t = d -v_2 \times t \\ d = v_1 \times t + v_2 \times t \\ d = t(v_1+v_2) \\ t = \frac{d}{v_1+v_2} \\ t = \frac{10.0}{100 + 42.0} = 0.0704 \;h \\ t = 0.0704 \times 60 \times 60 = 253 \;sec$