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solmaris [256]
3 years ago
13

A man walks along a straight path at a speed of 4 ft/s. A searchlight is located on the ground 20 ft from the path and is kept f

ocused on the man. At what rate is the searchlight rotating when the man is 15 ft from the point on the path closest to the searchlight
Mathematics
1 answer:
krek1111 [17]3 years ago
6 0

Answer:

0.128rad/sec

Step-by-step explanation:

Let x represent the between the man and the point on the path

θ = the angle

dx/dt = 4 ft/s

dθ/dt = rate is the searchlight rotating when the man is 15 ft from the point on the path closest to the searchlight

tan θ = x/20 ft

Cross Multiply

20tan θ = x

dx/dt = 20sec² θ dθ/dt

dθ/dt = 1/20 × cos² θ dx/dt

dθ/dt= 1/20 × cos² θ × 4

dθ/dt = 1/5 × cos² θ

Note : cos θ = 4/5

dθ/dt = 1/5 × (4/5)²

dθ/dt = 16/125

dθ/dt = 0.128rad/sec

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