Rocket question: A camera is mounted at a point 3000 ft from

[tebber]

A camera is mounted at a point 3000 ft from the base of a rocket launching pad. The rocket rises vertically when launched, and the camera's evelvation angle is continually adjusted to follow the bottom of the rocket.

a) Express the height x as a function of the elevation angle.

b) Find the domain of the function in part (a).

c) Plot the graph of the function in part (a) and use it to estimate the height of the rocket when the elevation angle is pi/4 (or 0.7854 radians). Compare this estimate to the exact height.

For part (a), I don't really even know what the question is asking me, but I think rgar rge function they want me to express is going to invole a delta to represent the changing angle.

For part (b), I'm not sure if they mean the angle cannot equal 0 because then the rocket would be on the ground, and it can't exceed 90 degrees.

For part (c), I think it's asking me to find which of sine, cosine, or tangent would work best to figure out the height. And I think its tan(45 degrees) and then x representing the opposite and the height of the rocket divided by 3000 the adjacent

If you have any advice to anything ive done or can answer any of the questions i have it would be VERY helpful

 

[galactus]

It would appear you're beginning related rates. You're on the right track.

By the diagram, use tan

Let \(\displaystyle {\theta}\)=angle of elevation


\(\displaystyle \L\\tan({\theta})=\frac{x}{3000}\)