How Do You Calculate Vertical Velocity and Energy Efficiency of a Ball Launcher?

[ilysukixd]

okay i have a question on determining the vertical velocity of a ball that leaves it launcher
i'm not sure if it is the initial vertical velocity on the lst part of trajectory
second question, how do you determine the kinetic energy of the ball at launcher(based on total initial energy v) and determine gravitational energy of the ball at launch
Last question how do you determine the energy efficiency of the launcher

 

[HallsofIvy]

okay i have a question on determining the vertical velocity of a ball that leaves it launcher
i'm not sure if it is the initial vertical velocity on the lst part of trajectory
second question, how do you determine the kinetic energy of the ball at launcher(based on total initial energy v) and determine gravitational energy of the ball at launch
Last question how do you determine the energy efficiency of the launcher

This is a physics question rather than a mathematics question so I am going to move it.

If you know the initial velocity of the ball, that, of course, determines the initial kinetic energy. If, instead, you know how the launcher accelerates the ball to that initial velocity, you can use the work done on the ball. For example, it the ball is lauched by a spring with spring constant k, pushing the ball over a distance d, then the work done is (1/2)kd and that is the initial kinetic energy.

The gravitational potential energy is given by mgh where h is the distance above what ever you take as reference point.

Finally, the "energy efficiency" is the kinetic energy of the ball as it is launched divided by the energy you had to put into the launcher (compressing the spring, pulling back the arm, etc.).