calc

A light is at the top of a pole 80ft high. A ball is dropped at the same height from a point 20ft from the light. If the ball falls according to 2=16t^2, how fast is the shadow of the ball moving along the ground 1 second later?

Let x be the distance of the shadow of the ball from the pole, on the ground. Draw yourself a picture and consider the two similar right triangles with side lengths (y,20) and (80,x).

y = the distance fallen, 16 t^2 (feet)

Clearly,
x/80 = 20/y
x = 1600/16 t^2 = 100/t^2
Solve for dx/dt @ t=1 s

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