{"id":11500,"date":"2022-07-12T22:50:55","date_gmt":"2022-07-12T17:20:55","guid":{"rendered":"https:\/\/mathemerize.com\/?p=11500"},"modified":"2022-07-12T22:50:59","modified_gmt":"2022-07-12T17:20:59","slug":"an-aeroplane-leaves-an-airport-and-flies-due-north-at-a-speed-of-1000-km-hr-at-the-same-time-another-aeroplane-leaves-the-same-airport-and-flies-due-west-at-a-speed-of-1200-km-hr-how-far-apart-will","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/an-aeroplane-leaves-an-airport-and-flies-due-north-at-a-speed-of-1000-km-hr-at-the-same-time-another-aeroplane-leaves-the-same-airport-and-flies-due-west-at-a-speed-of-1200-km-hr-how-far-apart-will\/","title":{"rendered":"An aeroplane leaves an airport and flies due north at a speed of 1000 km\/hr. At the same time, another aeroplane leaves the same airport and flies due west at a speed of 1200 km\/hr. How far apart will be the two planes after \\(3\\over 2\\) hours."},"content":{"rendered":"
Let the first plane starts from O and goes upto A towards north.<\/p>\n
Where OA = (\\(1000 \\times {3\\over 2}\\)) km = 1500 km<\/p>\n
Let the second plane starts from O at the same time and goes upto B towards west, where OB = (\\(1200 \\times {3\\over 2}\\)) km = 1800 km<\/p>\n
According to the question, the required distance = BA.<\/p>\n
In right triangle ABC, by Pythagoras theorem, we have :<\/p>\n
\\({AB}^2\\) = \\({OA}^2\\) + \\({OB}^2\\)<\/p>\n
= \\((1500)^2\\) + \\((1800)^2\\)<\/p>\n
= 2250000 + 3240000<\/p>\n
= 5490000<\/p>\n
AB = \\(3\\times 100\\sqrt{61}\\) = \\(300\\sqrt{61}\\).<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":" Solution : Let the first plane starts from O and goes upto A towards north. Where OA = (\\(1000 \\times {3\\over 2}\\)) km = 1500 km Let the second plane starts from O at the same time and goes upto B towards west, where OB = (\\(1200 \\times {3\\over 2}\\)) km = 1800 km According …<\/p>\n