Motion in two and three dimensions question?

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SUMMARY

The discussion centers on proving Galileo's principle that projectiles launched at angles equidistant from 45 degrees will have equal ranges, disregarding air resistance. The calculations involve horizontal and vertical components of projectile motion, specifically using the equations vx = v*cos(q) and vy_0 = v*sin(q) for initial velocities. The time of flight is derived as t = 2vy_0/g, leading to the determination of horizontal distance covered, which is essential for establishing the equality of ranges.

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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.
 
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You have found the duration of the flight. Now find the horizontal distance covered in the flight; this is the range in the question. The range will depend on the initial velocity and the angle of projection, so manipulate its formula to show what is required.
 

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