Speed of Rocket at 60 Degrees Elevation

[ProblemSets]

A rocket is rising vertically from a point on the ground 100 meters from an observer at ground level. The observer notes that the angle of elevation is increasing at a rate of 12 degrees per second when the angle of elevation is 60 degrees.

Find the speed of the rocket at that instant.

 

[robert Ihnot]

Since we know the cos(60) =1/2 and the length is 100 meters, the hypothesis is 200 meters. The height then 200sin(60) = 173.21 meters. This problem then can be done with the calculus and can be done without using it. Remember to change degrees into radians for the calculus.

 

[ProblemSets]

do u get 4800 m/sec?

 

[Feldoh]

I got 83.73 m/s

What do we want to figure out? The rate at which the rocket's height is changing, right? We want to find $$\frac{dy}{dt}$$.

We know:

$$\frac{d\theta}{dt}|_{\theta=\frac{\pi}{3}} = \frac{\pi}{15}$$

Solving using calculus you want to find an equation the relates the height to degrees with the given information, then find another equation that relates theta and the height with respect to time.