A Trig/Calc Problem

[cogman]

I Just thought this up, so I don't have the answer to it.

An airplane traveling at a constant speed of 150 km/h receives report that a tropical storm is heading its way. As the Pilot hears the report, he feels the wind start to pick up. The wind is coming in at a 90* angle from the airport and is accelerating at a constant speed of 20km/h^2. The airplane is 50 km from the airport. What is the rate at which the airplane will have to change its direction (in degrees) in order to keep a straight path to the airport. Will the airplane make it?

Again I just thought this up, so I don't even know if our Pilot will make it. (but Now I can start to work on it.) Enjoy.

[Spell checked, and wind acel changed to faster speed]

[dglienna]

without looking at his compass? :D

[cogman]

:). Im going to solve it now as I have nothing better to do. :) looks like I stumped this forum.

[cogman]

solved, But im A little leary of the answer I got. for those of you still that wish to do it look no further.




































































Ok, I came out with ~18.45* per sec would have to be the rate of change. with that knowledge, he would not have made it.

[dglienna]

you can try to solve my recursive math problem...

btw - it doesn't have to be done recursively, just have each number be different, except when it represents the same letter throughout the puzzle.

:D

[alkatran]

20 km/h^2 = 20*1000/60/60/60/60 m/s^2 = 0.00154 m/s^2

Plane speed: 150 km/h = 150*1000/60/60 = 41.7 m/s

Normal time to go 50 km:

50 000 / 41.7 = 1, 199s = 1/3 hours

Time for wind to reach the plane's speed:
150 / 0.00154 = 97, 402 s = 27 hours

Wind speed at .5 hours =
.00154*30*60 = 2.7 m/s

Angle at 2.7 m/s:
arcsin(2.7/150) = 1 degree

Something tells me they're gonna make it :afrog:


Oh, the rate is going to be very slow, but it won't be constant.