FILL IN THE BLANK!!!!!!!!!!!!!!!!!!!!!!! A man walks along a straight path at a
ID: 2838053 • Letter: F
Question
FILL IN THE BLANK!!!!!!!!!!!!!!!!!!!!!!!
A man walks along a straight path at a speed of 2 ft/s. A searchlight is located on the ground 4 ft from the path and is kept focused on the man. At what rate is the searchlight rotating when the man is 3 ft from the point on the path closest to the searchlight?
We draw the figure to the left and let x be the distance from the man to the point on the path closest to the searchlight. We let A be the angle between the beam of the searchlight and the perpendicular to the path.We are given that dx/dt = 2 ft/s and are asked to find dA/dt when x = 3. The equation that relates x and A can be written from the figure:
x/4 = tanA
x = 4 tanA
Differentiating each side with respect to t, we get dx/dt = 4 sec^2(A) * (dA)/(dt)
dA/dt = 1/4______ * dA/dt = 1/4_______ * 2 = ______ cos^2 (A)
When x=3, the length of the beam is 5, so cos(A) = 4/5 = ________
dA/dt = ______(______)^2 = ________
The searchlight is rotating at the rate of ________ rad/s.
Explanation / Answer
1) 32/25
2) 16/25
3)1/2
4) 0.9999025
5)(1/2)(cos)
6)4/5
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