simple physics q - velocity

[The_ArtofScience]

Hi

I am about to take Intro Physics this fall and I would like to get a few "what ifs" out of my mind. For starters, I have never been exposed to physics in hs (i choose the adv bio) so please be gentle

When an object of any sort attains a certain height gravity will pull the object down and height h= 1/2 gt^2. Velocity at some time t is = (v*sin$)/g and when its replaced back into the eq it becomes (v*sin$)^2/2g. Right? But when I draw a semicircle and label (x,y) on the x axis how does it "become" v^2sin(2$)/g?

I saw in a book the other day that the average of velocity can be calculated as follows: v_f^2-v_0^2 =2gs. Where does the v^2=2gs terms come from? I notice that when you flip things around you get s = v^2/2g which looks a little similar to t in f(t) for maximum height

Thanks

[Doc Al]

When an object of any sort attains a certain height gravity will pull the object down and height h= 1/2 gt^2. Velocity at some time t is = (v*sin$)/g and when its replaced back into the eq it becomes (v*sin$)^2/2g. Right? But when I draw a semicircle and label (x,y) on the x axis how does it "become" v^2sin(2$)/g?
Sounds like you are trying to derive the formula for the horizontal range of a projectile. Combine these two ideas: (1) The time of flight depends on the vertical component of initial speed; (2) The horizontal distance depends on the horizontal component of the initial speed.

To actually do this, you'll need to understand how to compute those quantities using the basic principles of kinematics.
I saw in a book the other day that the average of velocity can be calculated as follows: v_f^2-v_0^2 =2gs. Where does the v^2=2gs terms come from? I notice that when you flip things around you get s = v^2/2g which looks a little similar to t in f(t) for maximum height
That's not a formula for calculating average velocity. It's a kinematic relationship connecting velocity, distance, and acceleration.

Learn more about kinematic relationships here: Description of Motion in One Dimension (http://hyperphysics.phy-astr.gsu.edu/Hbase/mot.html#mot1); How they apply to trajectories is described here: Trajectory Concepts (http://hyperphysics.phy-astr.gsu.edu/Hbase/traj.html#tracon).