Calculus question. Is my work shown correct?

tanθ = y/x => y(1/x)

so, sec²θ.dθ/dt = (-1/x²)y.dx/dt + (1/x)dy/dθ

Now, as x is constant, dx/dt = 0 so,

sec²θ.dθ/dt = (1/x).dy/dt

Then, (1 + tan²θ).dθ/dt = (1/x).dy/dt

Now, when the rocket is at 41 feet, y = 35, x = 35 and dy/dt = 17 we have:

(1 + (35/35)²).dθ/dt = (1/35)(17)

Note: In your working, the dθ/dt on the left appears as dy/dt..??

so, 2.dθ/dt = 17/35

=> dθ/dt = 17/70

i.e. 0.243 radians/sec....all looks good.

P.S. It's always good to see someone's workings as it helps to highlight any errors and misconceptions..well done!!

:)>