Problem G
Flying Straight
A galloping horse travels at a constant speed on the Earth’s surface. However, because of the Earth’s curvature, the horse does not travel in a straight line in 3D space. Old Man Joe has a really special horse, named Joey, that can fly, but only in a straight line in 3D space. Old Man Joe wants to know how far apart Joey would be from a normal horse that gallops on Earth’s surface if they were to race for some time. Both horses start the race at the same location and start galloping/flying in the same direction (in particular, Joey flies in a straight line tangent to the Earth’s surface).
We will assume Earth is a stationary sphere with a radius of 6378137 meters.
Input
There is a single line of input containing three space-separated integers $F$, $G$, $T$, the speed of the flying horse in m/s, the speed of the galloping horse in m/s, and the number of seconds the race lasts, respectively. The numbers are such that $1\leq F, G \leq 10^{6}$, $1\leq T\leq 10^{8}$.
Output
Output the distance, in meters, between the two horses at the end of the race within $10^{-6}$ absolute or relative error.
| Sample Input 1 | Sample Output 1 |
|---|---|
1 1 1000 |
0.0783927968013984 |
| Sample Input 2 | Sample Output 2 |
|---|---|
19 20 300 |
300.0123889317558 |
