You and a highway patrolman are driving at constant speeds in opposite directions on a straight highway. The patrolman is driving at 60 mph and his radar gun determines your relative speed (the magnitude of the difference between your velocities) to be 135 mph. What is your speed at the time of measurement?

Question

Marks

Physics

18 January, 06:35

You and a highway patrolman are driving at constant speeds in opposite directions on a straight highway. The patrolman is driving at 60 mph and his radar gun determines your relative speed (the magnitude of the difference between your velocities) to be 135 mph. What is your speed at the time of measurement?

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Answers (1)

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Tristen Ferrell · Answer 1

Answer: 75 mph

Explanation:

The Relative Speed for a mobile is equal to the diference between the object and the observer:

Relative Speed (Rs) = Object's Velocity - Observer's Velocity

Thinking on those terms, we would need to have a universal observer to do any understandable measurement on daily basics. This is why we all use earth as a Static Observer for every measurement we do everyday.

Using Earth as an observer, the Velocity for the Patrolman is:

Patrolman Velocity (Vp) = 60 mph

Because the radar gun does measure the Relative Speed for the object, which is 135 mph, we need to work with the equation to find the Velocity using Earth as a reference.

Object's Relative Velocity = Object's Velocity - Patrolman's Velocity

Object's Velocity = Object's Relative Velocity + Patrolman's Velocity

We need to keep in mind, the Patrolman is going on the opposite direction. Because of this the sign for his velocity should be negative.

Object's Velocity = 135 mph + (-60 mph)

Object's Velocity = 135 mph - 60 mph

Object's Velocity = 75 mph