Question

1 2 An aeroplane at an altitude of 1 km is flying horizontally at 800 km/hr pasges directly over an. observer, find the rate at which it is preaching the observer when it is is 1250 meters away from him.​

Answer 1

$\huge\fbox\green{Answer}$

$h = 1000$

$x = \sqrt{1250 {}^{2} - 1000 {}^{2} }$

x = 750 meters horizontal

$r = distance$

$r {}^{2} = h {}^{2} + {x}^{2}$

$2r \: \frac{dr}{dt} = 0 + 2x \frac{dx}{dt}$

$\frac{dr}{dt} = ( \frac{x}{r}) \frac{dx}{dt}$

$\frac{dr}{dt} = ( \frac{750}{1250})800$

$\frac{dr}{dt} = 480$