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Range, Height and Time

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**Projectile Path All projectiles follow the same shape path.**

This path is a parabola. Acceleration is constant. Horizontal velocity is also constant. Velocity and position change.

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Parameterized Curve The two equations of motion can be combined to give an equation for the trajectory. We’ve set the origin to x0 = 0, y0 = 0.

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**Height The maximum height occurs when vy = 0.**

This is identical to 1-dimensional motion. From the height can the initial velocity be estimated?

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**Range The range of a projectile is the horizontal distance.**

The simplest range to find is for a projectile returning to its initial height. This is linked to the angle of the initial velocity.

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**Time The time in flight can be determined by height alone.**

The “hang time” is just this time in flight. A 1 m jump will be in the air for about 0.9 s. The range doesn’t matter.

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**Different Heights Not all motion starts and stops at the same height.**

The difference in height can be found by the full set of equations. Let y be some non-zero value.

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