I figured I'd come here to ATOT and see what I get.
I've got a question that is probably not extremely difficult to finish, I just can't think out of the box anymore. I'll list below this first question what I've done so far.
(1)
A ship is moving due west at 5 knots. You are in a speed boat at a distance of 7 nautical miles from the ship. Your bearing as seen from the ship is 102 degrees. You need to catch up with the ship. So you take off at a speed of 17 knots and a bearing of __________(a) degrees, and you reach the ship in ___________(b) minutes. Enter your answers as decimal expression with at least four digits, or enter mathematical expressions.
ANS:
(a) 278.7676399
t=time or rather the knotts variable
5t+7cos(12)
..\ ----------
...\.............|
....\............|
17t.\..........| 7sin(12)
.......\........|
.........\......|
...........\....|
............\...|
(*Yeah it's a crappy ASCII triangle, but I was going for understanding here...)
thus
(5t+7cos(12))^2+(7sin(12))^2=17t^2
or
264t^2-70tcos12-49=0
Throw that into the quadratic formula.
-b±sqrt(b^2-4(a)(c))/ 2(a) and you'll get t. Of which, I got the following answer.
t = 0.1524276704
Which is in hours, and I need it in minutes... So I calculate t(60) and get the following. 9.145660224 minutes, which doesn't work when I enter it in. Any help would be greatly appreciated.
PS -
Bearings in this case are.
N = 0 degrees
E = 90 degrees
S = 180 degrees
W = 270 degrees
I've got a question that is probably not extremely difficult to finish, I just can't think out of the box anymore. I'll list below this first question what I've done so far.
(1)
A ship is moving due west at 5 knots. You are in a speed boat at a distance of 7 nautical miles from the ship. Your bearing as seen from the ship is 102 degrees. You need to catch up with the ship. So you take off at a speed of 17 knots and a bearing of __________(a) degrees, and you reach the ship in ___________(b) minutes. Enter your answers as decimal expression with at least four digits, or enter mathematical expressions.
ANS:
(a) 278.7676399
t=time or rather the knotts variable
5t+7cos(12)
..\ ----------
...\.............|
....\............|
17t.\..........| 7sin(12)
.......\........|
.........\......|
...........\....|
............\...|
(*Yeah it's a crappy ASCII triangle, but I was going for understanding here...)
thus
(5t+7cos(12))^2+(7sin(12))^2=17t^2
or
264t^2-70tcos12-49=0
Throw that into the quadratic formula.
-b±sqrt(b^2-4(a)(c))/ 2(a) and you'll get t. Of which, I got the following answer.
t = 0.1524276704
Which is in hours, and I need it in minutes... So I calculate t(60) and get the following. 9.145660224 minutes, which doesn't work when I enter it in. Any help would be greatly appreciated.
PS -
Bearings in this case are.
N = 0 degrees
E = 90 degrees
S = 180 degrees
W = 270 degrees
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