What determines how far and how long an object will travel when hit?

if i was to throw a tennis ball apart from the weight of the ball, how would the speed my arm was going and the force i put into it when throwing the ball would affect how fast and how far and how long it will travel?What determines how far and how long an object will travel when hit?
The range equation R = V^2/g sin(2theta); where R is the distance an object will travel when launched at V speed and angle theta wrt the horizon. Clearly the initial velocity when hit determines the range R. Also the elevation angle theta determines that as well.





Note R is the range without drag. If there is drag the range r %26lt; R will be somewhat less than R. Even so, both V and theta have an impact on the range. Also note when theta = 45 deg, so that 2theta = 90 deg, the range R is the maximum range for any given V. This results because sin(90) = 1.000 and that's as large as a sine function gets.





Now getting V... V = F dT/m where F is the impact force if one is hitting the ball with mass m and dT is the length of the impact. So when hitting the ball hard (i.e., with as much force as you can) for a long time, the velocity will be higher than otherwise. This is one reason the coach tells you to keep the racket on the ball as long as you can... to increase dT and consequent V.





If you are simply throwing the ball, then clearly a faster hand-arm velocity will result in a faster initial tossed velocity. And that will result in a greater R, all other things equal.What determines how far and how long an object will travel when hit?
The only things that matter for how far the tennis ball goes are the initial speed and the direction it's going. The force you put on the ball determines how fast the ball is going when you release it. The force you put on the ball accelerates it until you let go. But if you were doing a physics problem, solving for how far the ball would go, the important things are the speed and direction it's thrown.





You can calculate that the best angle to throw a ball at to make it go farthest is 45 degrees.





Hope that helps