[4.1 Problem 38] You stand 40 ft from a bottle rocket on the ground and watch as it takes off vertically into theair at a rate of 20 ft/s. Find the rate at which the angle of elevation changes when the rocket is 30 ft in the air.Solution:40 ft20. We can see that 0 = tan- ().We are asked to find de when h =401600+h2dh30, given thatSOOP11 dh1+() 40 di40(20)1600+(30)2doWhen h = 30 we can see that *8002500(the units are radians per second).

[4.1 Problem 38] You stand 40 ft from a bottle rocket on the ground and watch as it takes off vertically into the air at a rate of 20 ft/s. Find the rate at which the angle of elevation changes when the rocket is 30 ft in the air.

[4.1 Problem 38] You stand 40 ft from a bottle rocket on the ground and watch as it takes off vertically into the air at a rate of 20 ft/s. Find the rate at which the angle of elevation changes when the rocket is 30 ft in the air.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.5: Trigonometric Graphs

Problem 28E

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Concept explainers

Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.

Question

[4.1 Problem 38] You stand 40 ft from a bottle rocket on the ground and watch as it takes off vertically into the
air at a rate of 20 ft/s. Find the rate at which the angle of elevation changes when the rocket is 30 ft in the air.
Solution:
40 ft
20. We can see that 0 = tan- ().
We are asked to find de when h =
40
1600+h2
dh
30, given that
SO
OP
1
1 dh
1+() 40 di
40(20)
1600+(30)2
do
When h = 30 we can see that *
800
2500
(the units are radians per second).

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