Asked by Steven
At a certain instant an aircraft flying due east at 240 miles per hour passes directly over a car traveling due southeast at 60 miles per hour on a straight, level road. If the aircraft is flying at an altitude of .5mile, how fast is the distance between the aircraft and the car increasing 36 seconds after the aircraft passes directly over the car?
Answers
Answered by
Steve
at time t=0,
let the plane be at (0,0,.5)
let the car be at (0,0,0)
let the +x axis be due east, so +y is due north
at time t hours,
plane is at (240t,0,.5)
car is at (60/√2 t,-60/√2 t,0)
the distance d between car and plane is
d^2 = (240t - 60/√2 t)^2 + (60/√2 t)^2 + .5^2
36 seconds = 0.01 hours, so
d^2 = (2.4-.6/√2)^2 + (.6/√2)^2 + .5^2
d = 2.0817
2d dd/dt = 7200(17-4√2)t
2(2.0817) dd/dt = 7200(17-4√2)(.01)
dd/dt = 196.16 mph
let the plane be at (0,0,.5)
let the car be at (0,0,0)
let the +x axis be due east, so +y is due north
at time t hours,
plane is at (240t,0,.5)
car is at (60/√2 t,-60/√2 t,0)
the distance d between car and plane is
d^2 = (240t - 60/√2 t)^2 + (60/√2 t)^2 + .5^2
36 seconds = 0.01 hours, so
d^2 = (2.4-.6/√2)^2 + (.6/√2)^2 + .5^2
d = 2.0817
2d dd/dt = 7200(17-4√2)t
2(2.0817) dd/dt = 7200(17-4√2)(.01)
dd/dt = 196.16 mph
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.