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Expert: - 3/3/2009


Question
I have one more question to finish this section.  Your help is greatly appreciated:  A light shines from the top of a streetlight 35 ft off the ground.  A ball is dropped from the same hieght 10ft away.  Assuming the ball falls 16t^2 ft in t sec, how fast is the ball's shadow moving 0.9 sec later?  Thanks so much.  Lori

Answer
Here we have similar triangles.

The height of the big triangle is H = 35 ft.

The height of the small triangle will be the height of the ball, which we will call X.

Put 0.9 in as t into 16t² and you will have the distance fallen F.
Take 32t and you have the speed S.

Subtract F from 35 and this will be the height of the small rectangle.

Note that the angle of the shadow is both 35/(10+x) and
(35-distance fallen)/x.

Let L be the length of the shadow, dL is the change in length.

We know H is 35 and can find x.  35/x is the same as (10+L)/L, so set them equal and solve for L.

We know that –X/5 =  dL/L.

X can be found, L can be found, and dL = -XL/5 by the last equation.

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