# Thread: speed of a rocket

1. ## speed of a rocket

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.

2. Notice when it is at 60 degrees up we can draw a 30, 60, 90 triangle which means the rocket will be 200 meters off the ground at this point

It took the rocket 5 seconds to get there so use the equation

$r = \frac{d}{t}$ where 200 is distance and 5 seconds is the amount of time it took.

3. whats the equation

4. Originally Posted by Mr_Green
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.
Draw a quick sketch. Call the horizontal distance from the observer to the point where the rocket takes off x (we know this is 100 m), and call y the vertical distance from the ground to the rocket. These are two legs of a right triangle, so the angle between x and the hypotenuse (the line of sight between the observer and the rocket) will be given by
$tan(\theta) = \frac{y}{x}$

So
$y = x~tan(\theta)$

When the angle $\theta$ is 60 degrees we know that the rate the angle is changing is 12 degrees per second. The question is asking, at that point in time, how fast is y changing? The answer is given by the first time derivative of y, which is equal to the vertical speed:
$v = \frac{dy}{dt} = x~sec^2{\theta}~\frac{d\theta}{dt}$

Edit: The rule above only works when $\theta$ is in radians. We need to convert 12 degrees/s into rad/s:
$\frac{d\theta}{dt} = \frac{12^o}{1~s} \cdot \frac{\pi~rad}{180^o} = 0.20944~rad/s$

So when $\theta$ is 60 degrees:
$v = 100 \cdot sec^2(60^o) \cdot 0.20944 = 83.7758~m/s$

-Dan

5. Hey Mr_Green? Do you go to SCN?

anyways...

i posted this same question on another forum and they provided me with the answer:

4189 m/sec

unfortunately they didn't show any work.

6. Originally Posted by DINOCALC09
Hey Mr_Green? Do you go to SCN?

anyways...

i posted this same question on another forum and they provided me with the answer:

4189 m/sec

unfortunately they didn't show any work.