Help with some easy engineering problems?

1.

http://s562.photobucket.com/albums/ss68/jintrater/...

β = arcsin(r/2/r) = arcsin(0.5) = 30° or 1/12th of the perimeter of each circle. Therefore, the perimeter of the two intersecting circles = 2(2πr)(1 – 4(1/12)) = 4πr(2/3) = 8/3πr.

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2.

140 mi/hr x 1609.3 m/mi x (1 hr/3600) sec = 62.6 m/s

At a height of 5’-9” (1.75 m) the signal travels 1.75/62.6 = 0.028 sec

Book drops 1 meter. 1 = (1/2)(9.8)t^2

t = 0.45 sec

Ratio = 0.45/0.028 = 16.07

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3.

The ribbon follows the path of an ellipse pulled out to become an elliptical spiral. The drop per wrap-around is 30/4 = 7.5 cm. So, the ellipse has a semi-major axis of sqrt(3^2 + 7.5^2) = 8.08. Semi-minor axis = 3 cm. The circumference = 19.15 cm. Since the ribbons goes around 4 times, its length = 4 x 19.15 = 76.6 cm.

http://www.csgnetwork.com/circumellipse.html