A police jeep chases a culprit on a motorbike. The motorbike crosses a turning at a speed of 72 km/h . The jeep follows at a speed of 90 km/h , crossing the turning ten seconds later than the bike. Assuming they travel at constant speeds, determine how far from the turning the jeep catches up with the bike, in km.

Step-by-step solution

Speed of the motorbike, v_m = 72 km/h = 72 5 18 = 20 m/s Speed of the police jeep, v_j = 90 km/h = 90 5 18 = 25 m/s The jeep crosses the turning 10 s after the motorbike. In this time, the distance covered by the motorbike is d₀ = 20 10 = 200 m Relative speed of the jeep with respect to the motorbike is v_ rel = 25 - 20 = 5 m/s Time taken by the jeep to catch up with the motorbike is t = 200 5 = 40 s Distance from the turning where the jeep catches the motorbike is d = v_j t = 25 40 = 1000 m = 1 km