Answer to Question #2774 in Abstract Algebra for carson
Suppose two gliders start at the same height, one with a glide ratio of 0.3 and one with a glide ratio of 2/7. If they glide until they hit the ground, which one will have glided the farther horizontal distance?
Let u=(ux,uy) be the coordinates of the initial velocity of the first glider, and v=(vx,vy) be the coordinates of the initial velocity of the second glider. Then by the definition glider ratio is the quotient: ux / uy = 0.3, vx / vy = 2/7
The move of each glider can be regarded as a sum of two moves: vertical and horizontal. The vertical move has negative acceleration a = -9.8 m/s^2, with initial velocity uy, while the horizontal move has constant velocity ux. Similarly for the move of the second glider.
Since& they hit the ground at the same moment T, starting from the same height, it follows that they come the same paths: Sy1 = uy * T& - g T^2 /2 Sy2 = vy * T& - g T^2 /2 As& S1=S2 and t is the same, it follows that uy=vy. Denote this number by& U.
Then& ux / U = 0.3, and thus ux = 0.3 U, and similarly vx=2/7 U.
Since the horizontal moves have constant velocities, we have that Sx1 = ux * T = 0.3 * U * T = 21/70 * U * T Sx2 = vx * T = 2/7 * U * T = 20/70 * U * T, so & Sx1 > Sx2
Hence the first glider come the farther horizontal distance.