Published on: Mon Feb 15 2010
Once again, there where many pictures in class. I’m going to summarize the basic formula’s and idea’s from today’s class. Just look at the sketches in the paper notes. Projectile motion forms a parabola. The object’s velocity forms a tangent of the x velocity and the y velocity. Y velocity is generally subject to gravity. The two components are independent of each other. x does not care about y and y doesn’t care about x either.
Note: My equation editor seems unable to draw an arrow on top of a letter.
1. Tangent of initial angle theta is equal to the initial Velocity of the vector, which is equal to the initial velocity of the y component over the initial velocity of the x component.
2. The magnitude (length) of the initial Velocity Vector is equal to square root of A squared plus B squared. (Pythagoras)
3. The velocity in x direction at time t does not change.
4. The x coordinate is equal to the initial x velocity times time.
5. The Velocity in the y direction is equal to the initial velocity minus acceleration caused by gravity times time.
6. The y coordinate is equal to the initial position plus initial velocity times time minus gravity times time squared.
7. The y position as a function of x is equal to x times tangent of theta minus, gravity times positive squared, divided by two times initial velocity of the x factor squared.
8. Range is equal to two times the sin of theta times initial velocity squared, divided by g.
9. Height is equal to the range divided by two.
10. The maximum range is equal to initial velocity squared times gravity.