Question

A state trooper is hidden 30 feet from a highway. One second after a truck passes; the angle θ between the highway and the line of observation from the patrol car to the truck is measured.


a. If the angle measures 15˚, how fast is the truck traveling?

b. If the angle measures 20˚, how fast is the truck traveling?

c. If the speed limit is 55 miles per hour and a speeding ticket is issued for speeds of 5 miles per hour or more over the limit, for what angle should the trooper issue a ticket?

Answer 1

the distance travelled by the truck is \[\frac{30}{\tan (15)}\]
You know the time it takes for the truck to cover this distance (1 second) hence the speed for the truck in that time is just the distance above divided by 1, which is your distance.

Answer 2

why not 30tan(15)

Answer 3

since the distance traveled by the truck is "opposite" and the 30 is "adjacent" from the angle 15 of the trooper.

still, since I was changing lanes toward the trooper during that interval I hope that the cop is ready to deal with my mathematician-lawyer

Answer 4

the ine of observation forms the hypotenuse, the opposite is the 30ft and then the adjacent is the distance to be found, x. So tan 15 = 30/x --> x = 30/tan 15

Answer 5

well, i'm assuming the truck is hidden at a distance of 30ft which is perpendicular to the highway, and that the highway is straight (we hope lol)

Answer 6

(b) is very similar and for (c) you need to solve for A: \[\frac{30}{\tan (A)} = 60\]
unless the policeman decides he wants to change his line of observation, which we hope not..

Answer 7

oh wait that's incorrect, you must convert 60mph to ft/hr. Similarly, your other speeds are in ft/hr, you would need to convert feet to miles to get them in mph.

Answer 8

sorry, your other speeds are in feet/sec. You would need to convert 60mph into ft/sec.

Answer 9

thank you so much ^^