Thank you <33
There are some missed details the knowledge of which can help very much...
a) what is the wheight of the missile at the time t=0?...
b) what is the 'rate of combustion' of the fuel in kilograms?... is this rate constant with time?...
c) what is the 'propulsive boost' of the missile in kilograms?... is that constant with time?...
d) is air resistance negligible?...
Kind regards
$\displaystyle \chi$ $\displaystyle \sigma$
Yes, start with a drawing, in this case a right triangle with base 5 and angle of elevation theta. Call the height s.
The relation between s and theta probably very useful...
$\displaystyle s = 5 \tan \theta$
Just in case a picture also helps with the logic of related rates... You might want to try filling up this pattern...
... where straight continuous lines differentiate downwards (integrate up) with respect to the main variable (in this case time), and the straight dashed line similarly but with respect to the dashed balloon expression (the inner function of the composite which is subject to the chain rule).
So differentiate with respect to the inner function, and the inner function with respect to t. Then sub in the given value of $\displaystyle \frac{d\theta}{dt}$ and $\displaystyle \theta$.
Spoiler:
__________________________________________
Don't integrate - balloontegrate!
Balloon Calculus: Standard Integrals, Derivatives and Methods
Balloon Calculus Drawing with LaTeX and Asymptote!
Double d'oh! The differentiation formula for tan does assume radians, so if we want to sub in an angle in degrees it'll affect the chain rule too...
So that's why.
Anyway... mods, very grateful if you can restore the original post, as Mr F was able to do on a previous occasion - for which, thanks.