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Projectiles
Summary
- A projectile is any object …
- with an initial non-zero, horizontal velocity
- whose acceleration is due to gravity alone.
- The path of a projectile is called its trajectory.
- A projectile is said to be …
- a simple projectile if the acceleration due to gravity may be assumed constant in both magnitude and direction throughout its trajectory.
- a satellite if it follows a closed path that never brings it in contact with a celestial body (like the earth).
- a general projectile no matter where its trajectory may take it.
- The kinematic equations for a simple projectile are those of an object traveling with …
- constant horizontal velocity and
- constant vertical acceleration.
| |
| horizontal |
vertical |
|
| ax |
= 0 |
ay |
= −g |
acceleration |
| vx |
= v0x |
vy |
= v0y − gt |
velocity-time |
| x |
= x0 + v0xt |
y |
= y0 + v0yt − ½gt2 |
displacement-time |
| |
|
vy2 |
= v0y2 − 2g(y − y0) |
velocity-displacement |
| |
- The horizontal distance traveled by a projectile is called its range.
- A projectile launched on level ground with an initial speed v0 at
an angle θ above the horizontal …
- will have the same range as a projectile launched with an initial
speed v0 at 90° − θ. (Identical
projectiles launched at complementary angles have the same range.)
- will have a maximum range when θ = 45°.
