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# Range, Height and Time PowerPoint PPT Presentation

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.

Range, Height and Time

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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.

### 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

• The maximum height occurs when vy = 0.

• This is identical to 1-dimensional motion.

• From the height can the initial velocity be estimated?

### 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.

### 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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