Question

An aeroplane at an altitude of 1 km is flying horizontally at 800 km/hr. passes directly over an observer. Find the rate at which it is approaching the observer when it is 1250 meters away from him ?

Answer 1

$h=1000$

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

$x=750$ metres horizontal

r=Distance

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

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

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

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

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