Angle of line of sight for a vertically lauched rocket

In summary, the problem involves finding the rate at which the angle of elevation needs to change in order to keep the rocket in the binoculars. This can be found by using the function arctan((60t-5t^2)/100) and differentiating it to find the rate of change of the angle, which is in radians.
  • #1
ziddy83
87
0
Hey...whats up,
ok... here's the problem.

A rocket is launched vertically from a point on the ground that is 100 horizontal meters from an observer with binoculars. The rocket is rising vertically and its height above the ground (in meters) is given by : [tex] y(t)=60t-5t^2 [/tex]
Two seconds after launch, how fast must the observer change the angle of elevation of her line of sight to keep the rocket in the binoculars?

I drew out the figure and...i know that i need to somehow compare the rate of change of the height of the rocket and the angle of her line of sight. So the rate of change of the height is y ' , which i got [tex] y' = t - 10t[/tex]

now how can i relate the two? I can plug in 2 seconds in y' to get the rate at which the height is changing, but what about the angle? as always, any help would be awesome.
 
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  • #2
Hints:
[tex] \tan{angle} = y(t)/100 [/tex]
And you want to know d(angle)/dt at t=2
 
Last edited:
  • #3
ok, correct me if I am wrong (which i think i am)...so to relate the two, the height and the angle, i can use the following function, [tex] arctan (\frac {60t-5t^2} {100})[/tex]
and then differentiate that to find the rate of change of the angle, right? :uhh:
 
  • #4
yeap, you got it, but remember the angle is in radian instead of degree
 
  • #5
great...thanks a lot you guys
 

1. What is the angle of the line of sight for a vertically launched rocket?

The angle of the line of sight for a vertically launched rocket is 90 degrees. This means that the rocket is being launched straight up from the ground.

2. Does the angle of the line of sight affect the trajectory of a rocket?

Yes, the angle of the line of sight does affect the trajectory of a rocket. The angle determines the initial direction and height of the rocket's flight, which influences its path and eventual landing location.

3. Can the angle of the line of sight be adjusted during a rocket launch?

Yes, the angle of the line of sight can be adjusted during a rocket launch. This is often done with a guidance system or by manually adjusting the launch mechanism. Changing the angle can alter the flight path and destination of the rocket.

4. How does air resistance affect the angle of the line of sight for a rocket?

Air resistance, also known as drag, can affect the angle of the line of sight for a rocket by slowing down its ascent and changing its trajectory. Stronger air resistance can cause the rocket to tilt and deviate from its intended path.

5. How is the angle of the line of sight calculated for a vertically launched rocket?

The angle of the line of sight for a vertically launched rocket can be calculated using trigonometry. The tangent of the angle is equal to the height of the rocket divided by the distance traveled along the ground. This can be used to determine the angle needed for a specific flight distance or height.

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