A cop sits in a parked car 10 feet from a straight road. As you drive along the road, the cop aims a radar gun at your car. Let s be the distance from your car to the cop in feet. The radar gun measures the rate at which your distance from the cop is changing with respect to time, which is ds/dt. Let x be the distance, in feet, of your car from the point on the road that is closest to the cop, so your car's velocity is dx/dt. dx (a) Draw and label a diagram of this scenario, and write dt ds in terms of s, and x. dt' ds dt ds dx (b) Use part a to explain why < Thus the radar gun's measurement of dt dt always underestimates your car's velocity. (This is why if the radar gun measures a speed greater than the speed limit on the road, the driver deserves a ticket.) (c) Does the conclusion in part (b) depend on the cop's car being 10 feet, rather than some other (positive) distance, from the road?