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January 27, 2015

January 27, 2015

Posted by **Anonymous** on Sunday, March 25, 2012 at 2:17pm.

- calculus -
**Steve**, Sunday, March 25, 2012 at 3:38pmlet x be the angle

let d be the distance of the dot from the point on the wall closest to the light

tan(x) = d/9

sec^2(x) dx/dt = 1/9 dd/dt

dd/dt = 1/9 sec^2(x) dx/dt

dx/dt = 4*2pi/min

I assume x = 5°, since 5 radians would point away from the wall.

dd/dt = 9 * 1.00765 * 25.13274 = 227.843 mi/min * 60min/hr = 13670.6 mi/hr

Check for sanity. If the wall were a circle 9 miles in radius, the circumference of the wall would be 9*2pi = 56.5 miles. That distance would be covered 4 times per minute, making the dot travel at a constant speed of 13572 mi/hr.

That would be the slowest speed observed when traveling along a straight wall, at the instant when the dot is closes to the light. Since 5° is a small angle, we'd expect the speed to be close to that figure, and it is, but slightly faster.

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