Hello everyone I am stuck on this question that I am facing. The question is that an individual was driving down a 120 feet road and found himself in a speedtrap. A police officer was parked 50 feet across the road and he gave the driver a ticket. The officer stated that the driver was going 65 mi/hr in a 55 mi/hr zone. The driver said that he was not going over 60 mi/hr. I tried to prove that he was going only 60 mi/hr but I cannot see how it can be done. From using the Pythagorean theorem I found the hypotenuse (distance from the car to police officer) to be about 130 ft. I made a second triangle with one leg being the 60 mi/hr (speed driver claims to be going) and the hypotenuse being 65 mi/hr (speed the officer ticketed the driver), the 2nd leg was found to be 25 mi/hr. I suppose this is a rate of change type of problem but I still do not see how it can be used to prove whether or not the driver was going 60 mi/hr. I am quite confused on it but thanks to everyone that will attempt to help me understand how to approach this problem better.
Speeding ticket question, calculus related?
- Thread starter alko18
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I don't understand what you're doing with the right triangle whose legs are speeds...? Please provide the exact text of the exercise, along with whatever assumptions, formulas, techniques, etc, that you are expected to apply. When you reply, please clarify what is meant by "a 120 feet road".
Note: Were this a "real life" situation, very much more documented information would be necessary in order even to begin to come close to "proving" a rate of speed. Your homework exercise, necessarily, represents a huge simplification on reality.
Note: Were this a "real life" situation, very much more documented information would be necessary in order even to begin to come close to "proving" a rate of speed. Your homework exercise, necessarily, represents a huge simplification on reality.
If the radar speed is measured at an angle, the measurement will be less than the actual speed. The radar only measures the component of the velocity vector that is directly toward or away from the observer.
In this case, Pythagoras gives the distance from Cop to Driver = 130 ft, and then by similar triangles
\(\displaystyle v = \dfrac{130\ ft}{120\ ft}(65\ mph) = 70\ mph \)
