Projectiles
A projectile is defined as any object in free fall, which means only affected by gravity. A golf ball flying through the air, a leaf falling from a tree, or a child jumping up and down are all examples of objects in free fall. The path that the object follows is known as a trajectory. Note: everything that I mention will be in a vacuum, which has no air resistance.
When a projectile is thrown along Earth’s surface, it follows a parabolic trajectory and eventually returns to the surface. During its flight, it is under constant acceleration, called acceleration due to gravity. On Earth, that value is 9.8 meters/sec/sec, or 32.2 ft/sec/sec. On the moon, where the force of gravity is much weaker, the constant acceleration is 1.625 m/sec/sec or 5.3 ft/sec/sec, or roughly 1/6th that of our gravity here on Earth.
In projectile motion, looking at both independent motions along the x and y axes, which are called rectilinear motions, is helpful. In the x-axis, the object's velocity stays constant for the duration of the trajectory, meaning there is no acceleration in the x direction. In the y-axis, acceleration is constant, and the velocity changes according to the acceleration.
where v is final velocity, v0 is initial velocity, a is acceleration, t is time, and Δx is horizontal displacement.
These equations can also be used in half projectiles, which are projectiles that start or end at their peak height, like throwing a ball horizontally off a cliff.
When you plot P(t), or position over time, the derivative of the graph will be V(t), or velocity over time. The derivative of V(t) will be acceleration, A(t), which will almost always be linear.
There are two different types of variables in physics: vectors and scalars. Vector quantities are known to have both direction and magnitude (size) and can be represented with a vector, whereas scalars have only magnitude. Path length is a scalar quantity that represents the distance an object traveled in a given moment. Displacement on the other hand is a vector quantity that is the total change in distance between the first and last points. So if you walked 1 mile in a circle, your path length would be 1 mile, but your displacement would be 0 because you ended at the same place you started. Speed is another scalar quantity, as it does not show direction, where velocity and acceleration are vectors. Time is scalar.
When looking at projectile motion, velocity, displacement, time, and acceleration are the main variables to know. Velocity is usually split into final and initial velocities, which makes 5 variables. Using these just 3 of these variables, you can find all 5 using Galileo’s equations:
