Multiple choice

Two aeroplanes left the airport at same time. First travelled at 22 kmph in the direction of 3500. The second travelled at 29 kmph in the direction of 2200. If both maintains their speed and direction, find the distance between them after 5 hours.

  1. 223.23 km

  2. 228.2 km

  3. 231.58 km

  4. 308.2 km
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C Correct answer
Explanation

The planes travel at 22 kmph and 29 kmph for 5 hours, covering 110 km and 145 km. The angle between 350 degrees and 220 degrees is 130 degrees. Using the law of cosines: d^2 = 110^2 + 145^2 - 2 * 110 * 145 * cos(130). d = sqrt(12100 + 21025 - 31900 * (-0.6427)) = sqrt(33125 + 20502) = sqrt(53627) = 231.575 km.

AI explanation

Using the formula Distance = Speed x Time, the first aeroplane travels 22 x 5 = 110 km and the second aeroplane travels 29 x 5 = 145 km in 5 hours. The angle between their flight paths is 350 degrees minus 220 degrees, which equals 130 degrees. Applying the cosine rule, the distance between them squared equals 110 squared plus 145 squared minus 2 x 110 x 145 x cos(130 degrees), yielding a distance of approximately 231.58 km. The result is 231.58 km.

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