
Concept explainers
Finding the Speed of a Truck A state trooper is hidden 30 feet from a highway. One second after a truck passes, the angle between the highway and the line of observation from the patrol car to the truck is measured. See the illustration.
(a) If the angle measures , how fast is the truck traveling? Express the answer in feet per second and in miles per hour.
(b) If the angle measures , how fast is the truck traveling? Express the answer in feet per second and in miles per hour.
(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 angles should the trooper issue a ticket?

To find:
a. If the angle measures , how fast is the truck traveling? Express the answer in feet per second and in miles per hour.
Answer to Problem 57AYU
a. .
Explanation of Solution
Given:
From the figure the distance between trooper and highway is 30 feet which is opposite to the elevation angle.
Formula used:
Calculation:
a. Angle of elevation measures .
So we need to find adjacent side so that we can know how far truck passes.
So we have to use ratio to find the adjacent side,
.
So in one second the truck travelled a distance of feet so the speed of the truck is feet per second,
1 feet per second miles per hour.
For miles per hour.

To find:
b. If the angle measures , how fast is the truck traveling? Express the answer in feet per second and in miles per hour.
Answer to Problem 57AYU
b. .
Explanation of Solution
Given:
From the figure the distance between trooper and highway is 30 feet which is opposite to the elevation angle.
Formula used:
Calculation:
b. Angle of measures .
So we need to find adjacent side so that we can know how far truck passes.
So we have to use ratio to find the adjacent side,
.
So in one second the truck travelled a distance of feet so the speed of the truck is feet per second,
1 feet per second miles per hour.
For miles per hour.

To find:
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 angles should the trooper issue a ticket?
Answer to Problem 57AYU
c. A ticket is issued if .
Explanation of Solution
Given:
From the figure the distance between trooper and highway is 30 feet which is opposite to the elevation angle.
Formula used:
Calculation:
c. 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.
So we can use ratio to find the angle,
A ticket is issued if .
Chapter 8 Solutions
Precalculus
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