Hello Sunyata Originally Posted by
Sunyata 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 $\displaystyle 4.9t^2$ m.
Thanks a lot!
Study the diagram I have attached. The distance $\displaystyle x$ m represents the distance of the shadow from $\displaystyle C$, the point directly below $\displaystyle A$, where the stone was dropped.
Using similar triangles: $\displaystyle \frac{RC}{BC}=\frac{RQ}{PQ}$
What you need to do now:Substitute into this equation the values I've given you in the diagram.
Solve for $\displaystyle x$ in terms of $\displaystyle t$.
Differentiate to find $\displaystyle \frac{dx}{dt}$. This represents the speed of the shadow.
Can you complete this now?
Grandad