Word Problem HELP!!

[jeca86]

A car is traveling at night along a highway shaped like a parabola with its vertex at the origin. The car starts at a point 100 m west and 100 m north of the origin and travels in an easterly direction. There is a statue located 100 m east and 50 m north of the origin. At what point on the highway will the car's headlights illuminate the statue?

 

[stapel]

To find the equation of the parabolic path y = a(x - h)² + k, note that (h, k) = (0, 0), and the point (-100, 100) lies on the curve.

Then note that the path of the headlights when the car is at any particular point (assuming the headlights are aimed straight ahead -- lawful adjustment would likely be too difficult to work with) will correspond to the tangent line at that point. The slope of that tangent line will be the derivative of the path's equation.

See if that helps you get started. If you have trouble finishing, please reply showing how far you have gotten. Thank you.

Eliz.

 

[jeca86]

word problem

Ok. So I have the value of a which is .01 or 1/100. Now I have to find the derivative. I have labeled the point I am looking for as P(f, f(x)). How do I set up my equation to find the derivative? Would I use my unknown point and the point of the statue?

 

[stapel]

I'm not sure what you mean by "setting up your equation" to find the derivative. You have "y = (quadratic)"; apply the derivative rule for polynomial terms.

Eliz.

 

[jeca86]

Thank you for helping me get through this problem. I don't know what the derivative rule for polynomial terms is. My trig teacher didn't mention that.

 

[stapel]

Derivatives, being part of calculus, would have been mentioned in your calculus class, not your trig class.

Eliz.

 

[jeca86]

Right, but my trig teacher likes to give us calc problems every once in a while so that we know what to expect when we do take calc.

 

[stapel]

...without the calculus tools necessary to answer the questions...? :shock:

I'm glad I didn't have your trig teacher! :roll:

If you don't know how to find derivatives, then I'm afraid I have no idea how your teacher is expecting you do to this. I'm very sorry.

Eliz.