1. Range, Height and Time

2. 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.

3. 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.

4. Height The maximum height occurs when vy = 0.
This is identical to 1-dimensional motion.
From the height can the initial velocity be estimated?

5. Fireworks
A fireworks shell is shot into the air with an initial speed of 70.0 m/s at an angle of 75.0º above the horizontal.
What is it’s maximum height?
S. Van Tonnigen, study.com
vy0 = 67.6 m/s
y = 233 m

6. 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.

7. Dud A fireworks shell is shot into the air and fails to ignite.
Initial speed of 70.0 m/s
Angle of 75.0º above the horizontal
How far away does the shell land?
S. Van Tonnigen, study.com
x = 250. m

8. 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.

9. Ignition
A fireworks shell needs a fuse that will ignite at the peak height.
Initial speed of 70.0 m/s
Angle of 75.0º above the horizontal
Height 233 m
How much time should the fuse have?
Up only
S. Van Tonnigen, study.com
t = 6.90 s

10. 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.