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Range, Height and Time. All projectiles follow the same shape path. This path is a parabola. Acceleration is constant. Horizontal velocity is also constant. Velocity and position change. Projectile Path. Parameterized Curve.

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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.

Projectile Path


Parameterized curve
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.


Height
Height

  • The maximum height occurs when vy = 0.

  • This is identical to 1-dimensional motion.

  • From the height can the initial velocity be estimated?


Range
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.


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.

Time


Different heights
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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