Can someone help me with this word problem? I think I solved it but my book doesn't have even number answers.
Problem:
Two commercial airplanes are flying at an altitude of 40,000 ft. along straight-line courses that intersect at right angles. Plane A is approaching the intersection point at a speed of 442 knots (nautical miles per hour; a nautical mile is 2,000 yards). Plane B is approaching the intersection at 481 knots. At what rate is the distance between the planes changing when A is 5 nautical miles from the intersection point and B is 12 nautical miles from the intersection point?
I got 614 nautical miles/hour (knots).
Problem:
Two commercial airplanes are flying at an altitude of 40,000 ft. along straight-line courses that intersect at right angles. Plane A is approaching the intersection point at a speed of 442 knots (nautical miles per hour; a nautical mile is 2,000 yards). Plane B is approaching the intersection at 481 knots. At what rate is the distance between the planes changing when A is 5 nautical miles from the intersection point and B is 12 nautical miles from the intersection point?
I got 614 nautical miles/hour (knots).
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x = 5 nm
dx/dt = -442 kt
y = 12 nm
dy/dt = -481 kt
s² = x² + y²
2sds/dt = 2xdx/dt + 2ydy/dt
ds/dt = (xdx/dt + ydy/dt)/s = [5(-442) + 12(-481)]/√(5²+12²)
ds/dt = (-7982)/13 = -614 kt
The distance is decreasing at a rate of 614 kt.
dx/dt = -442 kt
y = 12 nm
dy/dt = -481 kt
s² = x² + y²
2sds/dt = 2xdx/dt + 2ydy/dt
ds/dt = (xdx/dt + ydy/dt)/s = [5(-442) + 12(-481)]/√(5²+12²)
ds/dt = (-7982)/13 = -614 kt
The distance is decreasing at a rate of 614 kt.