Calculus

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A flower pot is dropped from a point 12 feet above the ground,so that it will land 4 feet from the base of a 12 foot lamppost. At what rate is the shodow of the flower pot moving along the ground when the pot is 8 feet above the ground?

• Calculus -

height y = 12 - 16t^2
shadow at x, similar triangles, so
x/12 = (x-4)/y
or,
xy = 12x - 48

y dx/dt + x dy/dt = 12 dx/dt
y=8 when t=1/2
x=6 when y=8

(12 - 16t^2) dx/dt + x (-32t) = 12 dx/dt
at t=1/2,
8 dx/dt - 96 = 12 dx/dt
dx/dt = 96/-4 = -24 ft/s

• Calculus - PS -

Oops.
x=12 when y=8

make the change and percolate it through the rest of the solution.

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