SOLVED: Suppose the lighthouse is located 3 km from the straight shoreline, and its light makes four revolutions per minute. How fast is the beam of light moving along the shoreline when it is 1 km from the nearest point on the shore? [Optional hints: Write θ in the diagram in terms of x. We want dx/dt when x = 1 km. What is dθ/dt? The answer is dx/dt = 80r/3 km/min:]
SOLVED: Suppose the lighthouse is located 3 km from the straight sho…
Oct 5, 2021
numerade.com
A lighthouse beam A lighthouse sits 1 km offshore, and its beam of light rotates counterclockwise at the constant rate of 3 full circles per minute. At what rate is the image of the beam moving down the shoreline when the image is 1 km from the spot on the shoreline nearest the lighthouse? | Numerade
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numerade.com
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A lighthouse is located on an island that is 2 mi off a straigh... | Filo
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A beacon on a lighthouse 1 mile from shore revolves at the rate of 10 πradians per minute. Assuming that the shoreline is straight, calculate the speed at which the spotlight is sweeping across the shoreline as it lights up the sand 2 miles from the lighthouse. (Hint: In Figure 3.39, x is the coordinate of the point on the shore at which the light shines. Thus d x / d t is the speed of the image of the spotlight moving across the shoreline, and d θ/ d t= 10 π.) | Numerade
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