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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.


Range height and 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.

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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