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Galileo shows that, if any effects due to air resistance are ignored, the ranges for projectiles on a level field whose angles of projection exceed or fall short of 45 degrees by the same amount are equal. Prove this result.
A: So ,I tried these vx = v*cos(q) //q is the shooting angle, vx is the speed in horizontal direction
vy_0 = v*sin(q) //original vertical speed
vy = vy_0 - gt // the projectile is pulled down by the gravity
----
x(t) = vxt
y(t) = vy_0t - 0.5gt^2
----
when the projectile hits the ground, y is 0
vy_0t = 0.5gt^2
vy_0 = 0.5gt
t = 2vy_0/g
How do I relate these altogether to prove the Galileo thing? Please.
A: So ,I tried these vx = v*cos(q) //q is the shooting angle, vx is the speed in horizontal direction
vy_0 = v*sin(q) //original vertical speed
vy = vy_0 - gt // the projectile is pulled down by the gravity
----
x(t) = vxt
y(t) = vy_0t - 0.5gt^2
----
when the projectile hits the ground, y is 0
vy_0t = 0.5gt^2
vy_0 = 0.5gt
t = 2vy_0/g
How do I relate these altogether to prove the Galileo thing? Please.