Question

Suppose a police officer is 1/2 mile south of an intersection, driving north towards the intersection at 50 mph. At the same time, another car is 1/2 mile east of the intersection, driving east (away from the intersection) at an unknown speed.a) The officer's radar gun indicates 30 mph when pointed at the other car (that is, the straight-line distance between the officer and the other car is increasing at a rate of 30 mph). What is the speed of the other car?b) Now suppose that the officer's radar gun indicates -30 mph instead (that is, the straight-line distance is decreasing at a rate of 30 mph). What is the speed of the other car this time?

Answer 1

The speed of the other car can be calculated using the concept of relative velocity. When the radar gun indicates 30 mph, the speed of the other car is 20 mph. When the radar gun indicates -30 mph, the speed of the other car is 80 mph.

Step-by-step explanation:

To find the speed of the other car in both scenarios, we need to use the concept of relative velocity. Let's break it down:

a) When the radar gun indicates 30 mph, it means that the straight-line distance between the officer and the other car is increasing at a rate of 30 mph. This is the relative velocity between the two cars. We know that the officer is driving north at 50 mph, so the relative velocity can be calculated as follows:

Relative Velocity = Speed of Officer - Speed of other car

30 mph = 50 mph - Speed of other car

Speed of other car = 50 mph - 30 mph = 20 mph

So, the speed of the other car is 20 mph.

b) When the radar gun indicates -30 mph, it means that the straight-line distance is decreasing at a rate of 30 mph. Again, we can calculate the relative velocity:

-30 mph = 50 mph - Speed of other car

Speed of other car = 50 mph - (-30 mph) = 80 mph

So, the speed of the other car is 80 mph this time.