How Does Doubling Initial Height Affect Projectile Range?

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Doubling the initial height of a projectile increases its range due to the extended time it spends in the air before hitting the ground. When a projectile is launched horizontally from a height of 2 feet versus 4 feet, the time to fall is determined solely by gravitational acceleration, which remains constant. This increased time allows the projectile to cover more horizontal distance. The relationship between height and range can be analyzed using kinematic equations. Understanding these principles is essential for calculating the effects of varying initial heights on projectile motion.
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What happens to range if the initial height is doubled. Say if something is shot at 2 ft and then its shot at 4 ft high, what happens to range? I know that its conservation of energy. I just have no idea how to come up with the right answer
 
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Plain kinematics can explain projectile range. A bullet shot horizontally will take a certain time to fall from height 2 ft to hit the ground. There's no initial vertical velocity so that time only depends on your acceleration. Use that time to find how far it goes.
 

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