Relate Rate help?

[mrjust]

The car is moving at 80 ft per second. The observer is 100 ft away from the road.
These is the drawing I was given at school and told to find angle x.
I'm supposed to find an equation f(t) (where t is time) such that f'(t) is maximized. I am stuck on finding an equation f(t) so that I can find its derivative. Honestly I don't know where to start.
I Appreciate all help.

 

[HallsofIvy]

At t= 0, the car is 500 feet from the point where there is a perpendicular from the observer to the road. Since the car is going 80 ft/sec, in t seconds, that distance will be 500- 80 t. You now have two legs, 100 ft and 500- 80 t ft, of a right triangle.

 

[Deleted member 4993]

View attachment 2745
The car is moving at 80 ft per second. The observer is 100 ft away from the road.
These is the drawing I was given at school and told to find angle x.
I'm supposed to find an equation f(t) (where t is time) such that f'(t) is maximized. I am stuck on finding an equation f(t) so that I can find its derivative. Honestly I don't know where to start.
I Appreciate all help.

First thing you have to do is to define - what do you need to find.

You said you need to find f(t) - a function of 't' - but what does that function describe?

Please share your work with us.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/th...217#post322217

We can help - we only help after you have shown your work - or ask a specific question (e.g. "are these correct?")

 

[mrjust]

I apologize, and thank you for you assitance. This is what I have gotten:

tan(x)=(500-80t)/100
x= arctan [(500-80t)/100]

Now I take the derivative

x'(t) = 1 / [ 1+ ((500-80t)/100^2)]*(-80/100)
x'(t)= 1 / [ 1 + (( 5 - 4t/5)^2)]*(-4/5) {I simplified}

Is these correct so far?

 

[Deleted member 4993]

I apologize, and thank you for you assitance. This is what I have gotten:

tan(x)=(500-80t)/100
x= arctan [(500-80t)/100]

Now I take the derivative

x'(t) = 1 / [ 1+ ((500-80t)/100^2)]*(-80/100)
x'(t)= 1 / [ 1 + (( 5 - 4t/5)^2)]*(-4/5) {I simplified}

Is these correct so far?

Your work is correct.

However, you wanted to find f(t) and f'(t) [according to your original post].

In the work above, you found x(t) and x'(t) - not what you wanted!!