Parabolic Projectile Paths

- The theoretical path for a fired object is a parabola
- You may remember parabolas from such courses as GCSE Mathematics – they’re various transformations of the y = x^2 curve
- Something fired at a steep angle will follow a tall, narrow parabola
- Something fired horizontally will follow a path that’s only half a parabola
- This assumes that the horizontal and vertical components of the vector are independent, and that there’s no air resistance or anything like that!
- You can use the SUVAT equations to calculate the distance, velocity, acceleration or time of the x and y components separately
- (See the SUVAT equations post)
- The initial velocity will be zero, because this thing was fired from rest
- (I guess projectiles can be fired from moving vehicles, but relative to the vehicle, the initial velocity is zero)
- Full parabolic paths are symmetrical, so if you know something about one half of the path, it’s probably true for the other (we’re ignoring air resistance, remember?)

Weight, Mass and Gravity

- Forces are vectors (see the vectors post), because they act in a direction
- Mass is a scalar, the amount of matter in an object. It’s not a force.
- Weight is the force that pulls things down. Not to be confused with mass.
- Gravity is an acceleration, not a force. It has magnitude g, 9.8 or 9.81 m s^-2 (on Earth, anyway) and acts in the direction towards the centre of the Earth (i.e. down)
- Newton’s second law, F=ma, states that force is the product of mass and acceleration
- Thus, weight = mass multiplied by gravity

Terminal Velocity

- Whilst we’re talking about stuff going down, I might as well mention it
- Terminal velocity is the velocity (in the downwards direction) at which the weight (force) is equal to the drag (air resistance, or whatever force is acting in the upwards direction), so the falling object stops getting faster and just goes at a constant speed
- That’s because the weight and drag are the same magnitude, in opposite directions, so there’s no resultant force and no acceleration (no vertical component, anyway)
- Newton’s first law states that an object will continue at a constant speed, until it’s acted upon by a (resultant) force
- Terminal velocity depends on weight and air resistance (so mass, gravity and cross-sectional area)

Miscellaneous

- You can add forces up to work out the resultant as described in my post on vectors
- When there’s a resultant force, there’ll be an acceleration, and vice versa (unless the mass is zero, I guess)
- The reaction force of a surface is the force with which a surface pushes back against something pushing against it
- I suppose that force is what explains why I’m not falling through the chair I’m currently sitting on
- The retarding force is the term for the combined effects of friction, air resistance, etc
- You can get forces generated by vehicles, etc, propelling them forward. I don’t know what they’re called. Propulsion or thrust, perhaps. Not “push” and “pull”, though.
- Is it me, or is “parabolic projectile paths” a tongue twister that gets easier the more times you say it quickly in a row?

###### Related articles

- SUVAT Equations – AS Physics Revision (mattg99.wordpress.com)

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