Question

I was wondering if anyone could help me on this question,

13. An airplane is flying on a level flight path at an altitude of 5 km. Shortly after it passes directly over an observation station, radar measures the straight line distance between them as 7.5 km, and finds that this distance is increasing at the rate of 735 km/hr.
a) How fast is the plane flying? b) How fast is the angle of elevation of the plane changing?

(It uses derivatives)

Thanks,

Answer 1

you know
\[y'=735\] and also that
\[y^2=x^2+5^2\] so
\[2yy'=2xx'\] and therefore
\[x'=\frac{yy'}{x}\]

Answer 2

plug in the numbers to find
\[x'\]

Answer 3

Oh okay though would we need to take into consideration the "straight line distance between them as 7.5 km"