I just want to check if my reasoning and answer are correct. The question is:
A rocket is launched straight up, and it's altitude is given by after seconds. You are on the ground 300m from the launch site watching the rocket going up. The line of sight from you to the rocket makes and angle with the horizontal. By how many radians per second is changing 10 seconds after the launch?
My reasoning is as follows:
Need to find
, so .
, so .
Remembering ,
Also, since , when .
Therefore,
So using Chain Rule:
Any help will be much appreciated.
Not what I got. It's basically a right triange with the the adjacent side to being 300m and the opposite side is the height, .
To relate all of them, you use TOA.
<< simplifying it a bit..
now we take the derivative of both sides with respect to time. Since is a variable, we have to use the chain rule.
now we plug in our numbers; make sure to use radians on your calculator; not degrees.
At , and using some trigonometry we find that . Use the memory function on your calculator!