Calculus Question

Question

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 elevation angle is continually adjusted to follow the bottom of the rocket.

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

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 = 0.7854 radian. Compare this estimate to the exact height.

Answer 1

A.  tanθ = x/3000,  so x = 3000tanθ

 

B.  0 ≤ θ < π/2

 

C. when θ = π/4, x = 3000tan(π/4) = 3000(1) =3000 ft