A plane flying horizontally at an altitude of 1 mile and a speed of of 500 mi/hr

Question

A plane flying horizontally at an altitude of 1 mile and a speed of of 500 mi/hr passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it is 2 mi. away from the station. is what is MIhr

Explanation / Answer

1 distance between radar and plane at time t s² = 2² + (vt)² 2sds/dt = 2v²t ds/dt = v²t/s at s = 2 25 = 4 + 500²t² 21/500² = t² ==> t=v21/500 h ds/dt = 500v21 /5 = 458.26 mi/h answer 458 mi/h ----------------- 2 distance between radar and plane at time t s² = (360tcos30)² + (3+360tsin30)² s² = 97200t² + (3+180t)² s² = 129600t² + 1080t + 9 2sds/dt = 2*129600t + 1080 sds/dt = 129600t + 540 ds/dt = (129600t + 540)/s at t = 1 minute = 1/60 h s² = 36 + 18 + 9 =63 ==> s = 7.937 ds/dt = (2160 +540)/7.937 = 342.18 answer : 342 km/h

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