Question

Rates of change question help. Will reward medal and fan. *Question attached below*

Answer 1

This is a classic related rates problem. Try making a picture like this (attached) and writing \(y\) as a function of \(x\). Since you're in a calculus course, you'll probably want to then differentiate afterwards or do something else calculus-y.

Answer 2

Do I need to subtract 1.6 from 8 m?

Answer 3

I can't see how that'd help, so probably not?

Answer 4

I'm sort of lost as to what I should do next

Answer 5

The two triangles are similar and right; try using proportionality to get \(y\) in terms of \(x\).

Answer 6

Ah, I'm as lost as someone who probably never did Calculus :(

Answer 7

The ratios of corresponding sides are equal whenever two triangles are similar. Which is to say,
\[\frac{x+y}{L}=\frac{y}{h}.\]

Answer 8

alrighty

Answer 9

But I have to find the rate?

Answer 10

Yep, differentiate implicitly with respect to time (be careful with the chain rule). Keep in mind that we were given \(\frac{dx}{dt}=1\).

Answer 11

I was never taught implicit differentiation

Answer 12

well, then solve for \(y\) in terms of \(x\). and differentiate both sides with respect to \(t\) (time).

Answer 13

Thanks