A beacon on a lighthouse is one mile from shore, and revolves at 10PI Radians per minute. What is the speed with which the light sweeps across the straight shore as it lights the sand 2 miles from the lighthouse?

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A beacon on a lighthouse is one mile from shore, and revolves at 10PI Radians per minute. What is the speed with which the light sweeps across the straight shore as it lights the sand 2 miles from the lighthouse?

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Answer 1 · 2015-06-05T16:54:57

The circumference of the circle being swept by the light at a distance of 2 miles is
$XXXX$ $color(white)("XXXX")$ $C = π \cdot 2 \cdot r a d i u s = π \cdot 2 \cdot (2) miles = 4 π miles$ $C = pi * 2 * radius = pi * 2*(2) " miles "= 4pi " miles"$
and represents $2 π$ $2pi$ radians

At a sweep rate of $10 π \frac{radians}{minute}$ $10pi " radians"/"minute"$

The speed of the distance swept at 2 miles is
$XXXX$ $color(white)("XXXX")$ $\frac{4 π miles}{2 π radians} \cdot \frac{10 radians}{minute}$ $(4 pi " miles")/(2 pi " radians") * (10 " radians")/("minute")$

$XXXX$ $color(white)("XXXX")$ $= \frac{20 miles}{minute}$ $=(20 " miles")/" minute"$

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A beacon on a lighthouse is one mile from shore, and revolves at 10PI Radians per minute. What is the speed with which the light sweeps across the straight shore as it lights the sand 2 miles from the lighthouse?

1 Answer

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