A light shines frm the top of a pole 50ft high.A ball is dropped frm the same height frm a point 30ft away frm the light.How fast is the shadow of the ball moving along the ground 1/2sec later?(Assume the ball falls s=16t^2ft in t sec)

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- Sep 29th 2007, 08:03 AMJoyceApplication of derivatives
A light shines frm the top of a pole 50ft high.A ball is dropped frm the same height frm a point 30ft away frm the light.How fast is the shadow of the ball moving along the ground 1/2sec later?(Assume the ball falls s=16t^2ft in t sec)

- Sep 29th 2007, 08:22 AMJoycehello
why nobody help?

- Sep 29th 2007, 08:28 AMearboth
hello,

I've attached a drawing of the situation.

You are dealing with 2 similar triangles. You can set up the proportion:

. Solve for y because that's the length which the shadow of the ball is away from the pole:

. You are told that . Substitute the variable s and you'll get the equation:

You know that speed is the first derivative wrt t of the length:

The speed at is:

- Sep 29th 2007, 08:32 AMearboth