Asked by Kristine
Francis starts walking north at 4 ft/s from an intersection I. At the same time Aram starts walking south at a
rate of 5 ft/s from a intersection 1500 ft due east of I. At what rate are they moving apart 15 minutes later?
(Rounding to 1 decimal place is fine.)
rate of 5 ft/s from a intersection 1500 ft due east of I. At what rate are they moving apart 15 minutes later?
(Rounding to 1 decimal place is fine.)
Answers
Answered by
Steve
the separation distance d at time t is given by
d^2 = (4t+5t)^2 + 1500^2
d^2 = 81t^2 + 2250000
2d dd/dt = 162t
d^2 at t=15min = 900 sec = 81*900^2 + 1500^2
= 100^2 * (81*81 + 15*15)
d = 100 * sqrt(6786)
d = 8237.719
dd/dt = 162(900)/16475.438 = 8.85
That looks reasonable. It's less than 9, but pretty close, since at 8237 ft apart, the initial 1500-ft separation is relatively small.
d^2 = (4t+5t)^2 + 1500^2
d^2 = 81t^2 + 2250000
2d dd/dt = 162t
d^2 at t=15min = 900 sec = 81*900^2 + 1500^2
= 100^2 * (81*81 + 15*15)
d = 100 * sqrt(6786)
d = 8237.719
dd/dt = 162(900)/16475.438 = 8.85
That looks reasonable. It's less than 9, but pretty close, since at 8237 ft apart, the initial 1500-ft separation is relatively small.
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.