Question

Related Rates 5. An air traffic controller spots two planes at the same altitude converging on a point as they fly at right angles to each other. One plane is 225 miles from the point moving at 450 miles per hour. The other plane is 300 miles from the point moving at 600 miles per hour. a). At what rate is the distance between the planes decreasing? b). How much time does the air traffic controller have to get one of the planes on a different flight path? 6. A patrol car is parked 50 feet from a long warehouse. The revolving light on top of the car turns at a rate of 30 revolutions per minute. How fast is the light beam moving along the wall when the beam makes angles of 70° with the perpendicular line from the light to the wall?

Answer 1

Solution. Two planes are at the same altitude Convenging on a point. Let, one of these planes. is x mides away from the point and another is y miles away from the point then distance between two planes as wartyr for the first plame, distance between the plane and the convenging point decnealing at a rate da - 600 miles/hour dt and that for the another plane decreasing at a rate auf - 450 mides 1 hour o rate of Change of distance between two planes, as = 2u du lan + y de la at 22x7 yr at * Cohen, r = 300, 72225 they are --600 feet-450 - 300 - 225 x1-450) √3004 225 W 300*225² = - 750 - Hence the distance between the planes de creasing at a rate - 750 miles thour Lany 5. (b). The time, the ain traffic Controlden have to get one of the plane on a diffenent flying path is a distance speed = 225 hour = h hour = 30min. Hence the Qin traffic controllen have 30 min deft. (Anl Scanned with CamScanner Scanned with CamScanner