Premium Online Home Tutors
3 Tutor System
Starting just at 265/hour
Answer :
Given,
Speed of first aeroplane = 1000 km/hr
Distance covered by first aeroplane flying due north in
\({1} {\dfrac{1}{2}}\) hours = 100 × \(\frac{3}{2} \) km = 1500 km
Speed of second aeroplane = 1200 km/hr
Distance covered by second aeroplane flying due west in
\({1} {\dfrac{1}{2}}\) hours (OB) = 1200 × \(\frac{3}{2} \) km = 1800 km
In right angle \(\triangle\) AOB, by Pythagoras Theorem,
\(\Rightarrow AB^2 = AO^2 + OB^2\)
\(\Rightarrow AB^2 = (1500)^2 + (1800)^2\)
\(\Rightarrow AB = \sqrt {(2250000 + 3240000)}\)
\( \Rightarrow AB = \sqrt{5490000}\)
\(\Rightarrow \) AB = \(300 \sqrt{61}\) km