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Calculus/Linear vs. Angular Speed
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Question
a patrol car is parked 50 feet from a long warehouse. the revolving light on top
of the car turns at a rate of 30 revolutions per minute. how fast is the light beam
moving along the wall when the beam makes the following angles with the line,
perpendicular to the wall, from the light to the wall? a. theta = 30 degrees
Partol car: 50 ft from wall
Light on top of car: revolving at 30 rev/min, which is 2π radians/minute
Angle beam is hitting wall at: 30° from straight on.
W: how far along the wall the beam is from straight over on wall from car
tan(Θ) = W/50 or W = 50tan(Θ).
W is increasing and Θ is moving, so they are both functions of t.
What we have is W(t) = 50tan[Θ(t)].
Taking the derivative gives W'(t) = 50secē(Θ)dΘ/dt.
W'(t) is what we are looking for.
secē(π/6) is known to √3/2.
dΘ/dt was given as 2π radians/minute.
W'(t) can be solved for with these two in feet / minute.
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Answers by Expert:
Scotto
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