Two airplanes are flying westward on parallel courses 9 mi apart. One flies at 425 mi/h and the other at 500 mi/h. How fast is the distance between the planes decreasing when the slower plane is 12 mi farther west than the faster plane?
2007-05-31 06:53:40 · 4 answers · asked by damalie m 1 in Science & Mathematics ➔ Mathematics
Relative motion.
Call the slower plane, A, and the faster one B.
vA/B = -75 mph due east.
Now the distance between them is 12 mi west and 9 mi north.
rA/B = 15.
θ = angle between west and rA/B.
d/dt (rA/B) = component of vA/B in the radial direction
= -75 * cosθ
= -75 * 12/15 = -60 mph
So the distance is decreasing at hte rate of 60 miles per hour.
2007-05-31 07:15:38 · answer #1 · answered by Dr D 7 · 1⤊ 0⤋
The distances between the planes can be described as the hypoteneuse of a triangle. Let the distance across the parallel, 9mi, be one leg (it's a constant). Then the length of the other leg is shrinking at a rate of 75mph (500-425)mph. if c^2=a^2+b^2=a^2+81mi^2, then
2c(dc/dt)=2a(da/dt)
dc/dt=a/c(da/dt)=12/(12^2+9^2)^ (1/2) * (75mph)=60mph
2007-05-31 14:22:46 · answer #2 · answered by supastremph 6 · 0⤊ 0⤋
Distance = sqrt(12-75t)^2+81) taking t=0 when the slower plane is 12 miles farther west
dD/dt= 1/2sqrt(12-75t)^2+81) * 2(12-75t)*(-75) which at t= 0 is
24(-75)/2sqrt(225) =-60 miles/h ( negativ because the distance is decreasing)
2007-05-31 14:14:55 · answer #3 · answered by santmann2002 7 · 0⤊ 0⤋
im going to say 60 mph....it has been a while since i have done a problem like this so i'm not 100% sure if its right
2007-05-31 14:03:59 · answer #4 · answered by Stop Sine 3 · 0⤊ 0⤋