Hi

How do I do this:

A lamp is 40 m above the ground and a stone is dropped from the same height at a point 10 m away. Find the speed of the shadow on the ground given that in t seconds the stone falls m.

Thanks a lot!

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- April 9th 2010, 06:24 AMSunyataConfusing Rates of Change
Hi

How do I do this:

A lamp is 40 m above the ground and a stone is dropped from the same height at a point 10 m away. Find the speed of the shadow on the ground given that in t seconds the stone falls m.

Thanks a lot! - April 9th 2010, 06:52 AMGrandad
Hello SunyataStudy the diagram I have attached. The distance m represents the distance of the shadow from , the point directly below , where the stone was dropped.

Using similar triangles:

Substitute into this equation the values I've given you in the diagram.Can you complete this now?

Solve for in terms of .

Differentiate to find . This represents the speed of the shadow.

Grandad - April 9th 2010, 07:56 AMSunyata
Ummm am I meant to get 4.9t^2x + 49t^2 = 400???

if so, when i implicitly differentiate that, I can't seem to get the answer... - April 9th 2010, 08:43 AMGrandad