Notes for Homework #13

Notes on parametric equations

Usually, we have a function with two variables, the dependent variable if either y or f(x) and the independent variable is x. In this case, we will instead have an independent variable t and two equations that are dependent on t, which in this case can be thought of as time measured in seconds. 

We will consider the path of a projectile being acted upon by gravity, where H(t) is the height and D(t) is the distance. We need two numbers to define our functions, v0 is the initial velocity - known as muzzle speed - and the angle at which the project is launched, which we will call theta. The two formulas are as follows, measuring time in seconds and height in feet

H(t) = t(sin(theta)v0 - 16t)
D(t) = t(cos(theta)v0)

Height will be 0 at t = 0 and when sin(theta)v0 - 16t = 0, which can be thought of as the launch and the landing, respectively.
When you solve the landing time, plug in that t into D(t) to get how far the projectile will travel before it hits the ground.


Notes on the angle between two vectors