Sigh.. Math..

[Ray-Chill]

You're flying from Joint Base Lewis-McChord (JBLM) to an undisclosed location 239 km south and 164 km east. Mt. Rainier is located approximately 56 km east and 40 km south of JBLM. If you are flying at a constant speed of 800 km/hr, how long after you depart JBLM will you be the closest to Mt. Rainier?

Seems easy?/
I've done this about 4 times..
And keep getting it wrong..
finally had to pick a different problem so it would change the numbers..
xD
Way to much work.

[bamag]

I think I kinda know how to do it. Do you have the answer so I can see if I'm doing it right?

[Ray-Chill]

Not for this exact problem.. xD
I can find it though..
You basicly have to find the function for the first line that goes from the air force base to (164, -239)
Then find the perpendicular line that goes through the point for the mountain..
Then find the point of intersection.
Then the distance formula.. Lol
All with way to many fractions..
xD

[Rain]

I got 4.85 hours. It's probably wrong, but I'm just throwing it out there.

[bamag]

Line to undisclosed location is y=-(239/164)x
Mt. Rainier is the point (56,-40)
That's what I got so far, lemme figure out the rest :p
You can optimize the thing so..
D = sqrt( (x-56)^2 + (y+40)^2 )
Substitute y for -(239/164)x...
D = sqrt ( (x-56)^2 + (-(239/164)x+40)^2 )
D^2 = (x-56)^2 + (-(239/164)x+40)^2
God this is disgusting D:

[Ray-Chill]

Sorry. the line formula is y=mx+b
=]
so for getting to where ever it would be y=-239/164x with no b because b is really the y-intercept.

[bamag]

Okay I'll approach in another way..
Shortest distance between point and line is:
d=|mx+b-y|/sqrt(1+m^2)
d = |(-239/164)(56)+0+40|/sqrt(1+(-239/164)^2
d = 6824/sqrt(84017)
Then use distance formula to find x,y , knowing y=-(239/164)x
Geez this problem is too messy..
x=3074016/84017
y=-4479816/84017
Distance from origin to that is ~64.66km.
64.66/800 = ~.08
So .08 hours.... I don't know if its supposed to be this complicated or I did something wrong T.T

[Rain]

Can you check the answers?

[bamag]

@(you need an account to see links) if its 4.5hours, thats 3600km lol. Doesn't seem like its even possible :o

[Rain]

Oh, omg, I just realised I did something really stupid. Thanks for pointing that out. ;D @(you need an account to see links)

---------- Post added at 11:37 PM ---------- Previous post was at 11:30 PM ----------

Ok, so I fixed it up, and got 0.08083541575, so basically 0.08, which is what you got.
I made the mistake of multiplying it by 60 afterwards. LOL. Idk why I did that.

Also, I didn't do it the way you did.