A camera is set up at the starting line of a drag race 60 ft from a dragster at the starting line (camera 1 in the figure). Two seconds after the start of the race, the dragster has traveled 120 ft and the camera is turning at 0.4 rad/s while filming the dragster. Answer parts a. and b. below. ---- Camera 2 Camera Dagster 60 ft a. Write an equation relating the distance the dragster has traveled, to the angle 0 through which camera 1 has turned to film it. b= 60 tan e Differentiate both sides of the equation with respect to t. db de - 60( sec 0)? dt dt What is the speed of the dragster at this point? The speed of the dragster is 120 ft/s. (Type an integer or a decimal.) b. A second camera (camera 2 in the figure) filming the dragster located on the starting line 110 ft away from the dragster at the start of the race. How fast is this camera turning 2 s after the start of the race? This camera is turning at a rate of (Round to three decimal places as needed.)

Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter4: Polynomials
Section4.8: Rate-time-distance Problems
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A camera is set up at the starting line of a drag race 60 ft from a dragster at the starting line (camera 1 in the figure). Two seconds after the start of the race, the dragster has traveled
120 ft and the camera is turning at 0.4 rad/s while filming the dragster. Answer parts a. and b. below.
Starting line
Camera 2
Camera 1
Dragster
60 ft
110 ft
a. Write an equation relating the distance the dragster has traveled, b, to the angle 0 through which camera 1 has turned to film it.
b = 60 tan 0
Differentiate both sides of the equation with respect to t.
db
de
( 60( sec 0)
dt
%D
dt
What is the speed of the dragster at this point?
The speed of the dragster is 120 ft/s.
(Type an integer or a decimal.)
b. A second camera (camera 2 in the figure) filming the dragster is located on the starting line 110 ft away from the dragster at the start of the race. How fast is this camera turning 2 s after the start of the race?
This camera is turning at a rate of
(Round to three decimal places as needed.)
Transcribed Image Text:A camera is set up at the starting line of a drag race 60 ft from a dragster at the starting line (camera 1 in the figure). Two seconds after the start of the race, the dragster has traveled 120 ft and the camera is turning at 0.4 rad/s while filming the dragster. Answer parts a. and b. below. Starting line Camera 2 Camera 1 Dragster 60 ft 110 ft a. Write an equation relating the distance the dragster has traveled, b, to the angle 0 through which camera 1 has turned to film it. b = 60 tan 0 Differentiate both sides of the equation with respect to t. db de ( 60( sec 0) dt %D dt What is the speed of the dragster at this point? The speed of the dragster is 120 ft/s. (Type an integer or a decimal.) b. A second camera (camera 2 in the figure) filming the dragster is located on the starting line 110 ft away from the dragster at the start of the race. How fast is this camera turning 2 s after the start of the race? This camera is turning at a rate of (Round to three decimal places as needed.)
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