A petrol car is parked 50 feet from a long warehouse (see figure). The revolving

Question

A petrol car is parked 50 feet from a long warehouse (see figure). The revolving light on loop of the car turns at a rate of 40 revolutions per minute. Find the velocity of the beam along the wall, when theta = 45 degree. 40 rev/min = rad/min Write theta as a function of x, using the correct inverse function, based on the given information shown: cosine, sine, or tangent; and then find dx/dt theta(x) = d theta/dt = To solve this problem, we must find what:(A: d theta/dt or B: dx/dt) Select the correct choice: A B How fast is the beam moving along the wall the beam makes an angle of theta = 45 degree(Remember: You cannot manipulate degrees)with the line perpendicular from the light to the wall? Also give the units to your answer, and spell the enter wording for the units/min.

Explanation / Answer

40 rev/min =40*2 rad /min

40 rev/min =251.3274 rad /min

(x)=tan-1(x/50)

d/dt =251.3274

we must find dx/dt

tan=x/50

differentiate with respect to time on both sides

sec2 d/dt =(1/50) dx/dt

dx/dt =50sec2 d/dt

dx/dt =50sec245o *251.3274

dx/dt =25132.74 ft /min

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