A police jeep is chasing a culprit going on a motorbike. The motorbike crosses a turning at a speed of 72 km/h. The jeep follows it at a speed of 90 km/h, crossing the turning ten seconds later than the bike. Assuming that they travel at constant speeds, how far from the turning will the jeep catch up with the bike?

#### Solution

Velocity of the police jeep,* **v*_{p} = 90 km/h = 25 m/s

Velocity of the culprit riding the motorbike,* **v*_{c} = 72 km/h = 20 m/s

In 10 seconds, the culprit reaches point B from point A.

Distance covered by the culprit:*s *= *v _{c}t* = 20 × 10 = 200 m

At time *t* = 10 s, the police jeep is 200 m behind the culprit.

Relative velocity between the police jeep and the culprit:

25 − 20 = 5 m/s

In 40 seconds, the police jeep moves from point A to a distance *s*' to catch the culprit.

Here,*s*' = *v _{p}t* = 25 × 40

⇒

*s*' = 1000 m = 1.0 km

Thus, the jeep will catch up with the bike 1.0 km away from the turning.