Same u_y, different u_x

• All three projectiles have the same vertical motion since they have the same initial vertical velocity u_y.
• Since the time of flight is the same, the horizontal range is proportional to horizontal velocity u_x.

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Same u_x, different u_y

• The maximum height is proportional to u_y².
• All three projectiles actually move forward at the same speed since they have the same horizontal velocity u_x.
• But the horizontal range is also dependent on u_y, resulting in the horizontal range being also proportional ot u_y.

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Same θ, different u

• Both the maximum height and horizontal range are proportional to u².

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Same u, different θ

• Increasing θ results in increasing u_y but decreasing u_x.
• The projectile launched at θ = 15° lands at the spot at the once launched at θ = 75°. This is because even though it moves forward at a higher speed, it stays in flight for a shorter time.
• The maximum range is attained at θ = 45°.

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• 02 Kinematics