Question

A robber is in a fast car, hurrying away from the scene of his crime. his car can go at 150 km/h. he will be safe if he can reach the border, 40 km away.

A police car arrives at the scene of the crime. the police are late! the robber has already travelled 10 km towards the border. the police car sets off in hot pursuit.

A) How far is the robber from the border at this time?

B) Calculate how long it will take the robber to reach the border.

C) How fast must the police cat travel if it is to catch the robber before he reaches the border?​

Answer 1

A) When the police arrived at the crime scene, the distance travelled by the robber is 10 km. So, the distance between the robber and the border would be 30 km.

B) If we calculate it from the time when the police hasn’t arrived yet, it would be:

v = (xf - xi)/t

Rearrange it :
t = (xf-xi)/v = (40 - 0)/(150) = 0.267 hour

C) First of all, let’s calculate the time the robber takes to arrive at the border

Note : we would assume at t = 0 is when the police arrived at the crime scene, so we will take the initial position of the robber when the robber has travelled 10 km towards the border.

So, the distance of the robber and the border would be 30 km. Thus, the time taken by the robber would be:

t = x/v = 30/150 = 0.2 hours

Next, we will use that time to calculate the speed of the police. So, that the police would use that speed to arrive at the border on the same time as the robber. So, the police can catch the robber :D

By using kinematic equation,

x = ((vf - vi)/2) t

where x is the distance of the crime scene and the border
vf is the final speed of the police to arrive at the border
vi is the initial speed of the police
t is the time taken by police to arrive at the border

(40 km) = ((vf - 0)/2) (0.2 hours)

40 = 0.1 vf

vf = 400 km/h

Hope this will help you :D