Two planes take off from the same airport at the same time using different runways. One plane travels on a bearing Upper S 14 degrees Upper W at 440 miles per hour. The other plane travels on a bearing Upper N 75 degrees Upper W at 420 miles per hour. How far are the planes from each other 3 hours after takeoff?

Question

Physics

Deegan Wang

15 October, 18:23

Two planes take off from the same airport at the same time using different runways. One plane travels on a bearing Upper S 14 degrees Upper W at 440 miles per hour. The other plane travels on a bearing Upper N 75 degrees Upper W at 420 miles per hour. How far are the planes from each other 3 hours after takeoff?

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Answers (1)

Know the Answer?

Brayan Chang · Answer 1

Let's imagine this is the diagram for the question,

•

3*440 = / |

/ |

1320mi ↑ |

↑ ↓

/ ↓

/ |

•) 89⁰ |

/ | "x" miles

/ ↑

/ ↑

↓ |

↓ |

3*420 = / |

1260 mi / |

•

From the Cosine Rule: x² = y² + z² - 2 y z cos X⁰

x² = 1320² + 1260² - 2 * 1320 * 1260 * cos 89⁰ =

1742400 + 1587600 - 3326400 * cos 89⁰ = 3271946315

x ≈ 1809 mi

Hence, the planes are 1809 miles from each other 3 hours after takeoff?