Finding Initial Velocity from Launcher Trajectory

[geolej]

Homework Statement

Find out the launch velocity from the launcher (the absolute starting point aka x=0)

Angle (degrees) Height(cm) Average Distance Traveld(cm)
0 99.0 220.73
30 104.3 307.8
45 106.6 380.4
60 108.5 319.2

Homework Equations

We were given a equation on the board, but I think I copied it incorrectly:

Vi=sqrt(gx^2/cos^2theta(xtantheta-y))

The Attempt at a Solution

I get a very wrong solution with said equation, because I know that the velocity should change.

 

[Fightfish]

Instead of wondering whether you copied the equation wrongly or not, why not attempt to derive it yourself? It's basic 2-d kinematics, and deriving the relation yourself will help you get a better understanding of what is going on than plugging and chugging values into some random equation.

 

[nocturnus]

Have you taken any physics or calculus courses? If you have, then look up basic kinematic equations and start from there. You have two unknowns... one is the time elapsed for each angle theta and each distance traveled, and the second unknown is the initial velocity. That means you need two equations. So you either need to solve for initial velocity first, or the time first because those are our only two options. The problem IS to find the initial velocity, so that leaves us with solving for the time elapsed.

Hint: At the top of the trajectory, the time elapsed is t/2. Use this fact to form one of the two equations you need.