Question

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 a constant speeds, how far from the turning will the jeep catch up with the bike ? Concept of Physics - 1 , HC VERMA , Chapter "Rest and Motion : Kinematics

Answer 1

Solution :

Speed of motor bike=72 km/hr=72x5/18 =20 m/s
Speed of Jeep=90x5/18=25m/s
Let us assume that Jeep catches the bike at a distance of  X m from the turning.
Time taken to civer  distance X m =Distance/time
=x/20 sec

Since jeep starts 10 sec later , so it takes 10s less time to cover the equal distance
Time taken to cover X m will be =x/20 - 10
But from the jeep's speed it comes to be x/25 s
These two must be equal. Hence
x/20-10=x/25
x-200/20=x/25
x-200/4=x/5
5x-1000=4x
x=1000m=1km

∴Hence the jeep will catch up the bike at a distance of 1km

Answer 2

HEY!!

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▶Velocity of the police jeep, vp = 90 km/h =
25 m/s

▶Velocity of the culprit riding the motorbike, vc = 72 km/h = 20 m/s

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

Distance covered by the culprit=
s = vct = 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

▶Time=Distance to be covered/Relative velocity = 2005 = 40s 

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

s = vpt = 25 × 40
s' = 1000 m = 1.0 km

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