An unexpected storm blows the ship to a point 5000 km due east of its starting point.
How far must it now sail to reach its original destination?
2007-09-05 07:37:21 · 6 answers · asked by Alexander 6 in Science & Mathematics ➔ Physics
For a spherical right triangle the equivalent of the Pythagorean theorem is:
cos(c) = cos(a)cos(b)
where a,b and c are the arc lengths of the legs and hypotenuse respectively. 5000 km is pi/4 radians according to one of the former definitions of the meter (which is still a close approximation) -->
cos(c) = cos(pi/4)^2 = 1/2
-->
c = pi/3
In meters that's (4/3)*5000 = 6666 km.
2007-09-05 16:26:57 · answer #1 · answered by shimrod 4 · 3⤊ 0⤋
5000 km east on the equator is approximately 45 degrees (1/8 of the circumference) of longitude. 5000 km due north from the equator is also approximately 1/8 of the circumference - at 45 degrees of latitude. At this latitude, 45 degrees of longitude covers approximately 3555 km.
Since all of these are approximations, we can continue with an approximation of a right triangle with sides of 5000 km and 3555 km. Which comes out to an approximate total distance now of 6135 km from your original destination.
2007-09-05 09:31:18 · answer #2 · answered by skeptik 7 · 0⤊ 0⤋
Imagine this on a diagram and it becomes a right angled triangle with the two shorter sides being 5000km.
This means Pythagoras Theorem can be used to find the distance
(5000^2+5000^2)^0.5 = 5000sqrt2 km
2007-09-05 07:41:49 · answer #3 · answered by SS4 7 · 0⤊ 2⤋
The deliver could desire to circulate in a path that's the consequent of two displacement vectors. One is a hundred km in the direction of west and the different is a hundred and twenty km in the direction of north. magnitude of required displacement = sqrt(a hundred and twenty^2 + a hundred^2) = sqrt(14400 + ten thousand) = sqrt(24400) = 156 km (after rounding off) enable the path be at attitude theta with west. Then tan(theta) = a hundred and twenty/a hundred = a million.2 Or theta = atan(a million.2) = 50.2 deg Ans: 156 km at 50.2 deg north of west
2016-11-14 06:49:12 · answer #4 · answered by mangiafico 4 · 0⤊ 0⤋
This is a triangle with 5,000 for one leg and 5,000 for the other. What is the hypotenuse??
There you go..........
If you are talking about the curve of the earth, it is more complicated, as you have to figure out the arc distances above the given chords..........
..
2007-09-05 07:42:52 · answer #5 · answered by muddypuppyuk 5 · 0⤊ 0⤋
In other words, they want you to find length of diagonal whose sides are 5000km. & 5000km.( square )
which is root 2 x 50000 or 1.414 x 5000 = 7070 km. Clear?
2007-09-05 07:45:37 · answer #6 · answered by Pandian p.c. 3 · 0⤊ 1⤋