Question

In addition, complete the following problem: Consider the car and radar gun that we discussed in class, as shown below. Suppose that θ- 20° and the radar gun measures 72 m.p.h. What is the actual speed of the car that you calculate? what happens as θ increases? Discuss how this impacts the accuracy of the radar gun (and whether you can use this information to argue your way out of a speeding ticket...).

Answer 1

The radar gun will be measuring the cos component of the velocity, Therefore we can write, (v is the actual speed)

$v cos \theta = v_{meas}$

Substituting values we get,

$\Rightarrow v cos (20^\circ) = 72 \, mph$

$\Rightarrow v (0.94)= 72 \, mph$

$\Rightarrow v = 76.6 \, mph$

As you can see from the above equation, as the angle increases. The speed measured by the speed gun decreases, This in turn reduces the accuracy of the speed measured by the gun. One more trick is to be far away from speed gun, then this will give a very high value of the angle, and the speed gun will be measuring lesser value, helping you to avoid tickets.