# Thread: hard related rates problem

1. ## hard related rates problem

a light is attached to the wall of a building 64 feet above the ground. a ball is dropped from the same height, but 20 feet away from the side of the building. the height y of the ball at time t is given by y(t)=64-16t^2. How fast is the shadow of the ball moving along the ground after 1 second?

2. Originally Posted by supaflyz88
a light is attached to the wall of a building 64 feet above the ground. a ball is dropped from the same height, but 20 feet away from the side of the building. the height y of the ball at time t is given by y(t)=64-16t^2. How fast is the shadow of the ball moving along the ground after 1 second?
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3. Why is that "hard". Get the geometry straight and you're on your way.

Think "Similar Triangles" and consider where the ball is and the line of sight for the shadow. You should get the following proportional parts.

Vertical Leg

64 - (Y(t)) vs 64

Horizontal Leg

20 vs {where the shadow meets the road}

Hypotenuse

Well, feel free to use the Pythagorean Theorem to get this one. You don't really need it. The first two are sufficient.

$\displaystyle \frac{20}{64-Y(t)}\;=\;\frac{Shadow}{64}$

Now what?