Homework Help: Projectile Motion of a Batter Problem

You should know that with any projectile problem like this, if the inital speed is v m/s, the angle is θ, and the initial height is h m, then the initial velocity vector is
v cosθi+ v sinθ j. The velocity vector at time t (in seconds after the "launch") is v cosθi+ (v sinθ-gt)j and the "position" vector at time t is
v cosθti+ (h+ v sinθt- (g/t)t²)j. The ball has range 107 m. I'm not at all clear what "returning to the level launch" means. I would assume that range was measured to the point where the ball hits the ground: where the j component of position is 0 but the height of the "launch" is 1.22 m!? Any way, you can set the vertical component of position to 0 (or 1.22?) and the horizontal component to 107 so that you have 2 equation to solve for the two unknown numbers v and t- except that you are right- you don't need to find t. If it is easier, go ahead and eliminate t from the two equations and just solve for v- that's what you need to know! Once you know a, put it into the equation for horizontal distance, with horizontal distance equal to 95.5 and solve for that t. Now put that t into the vertical distance equation, find the vertical height of the ball at that time and see if it is larger than 7.32 m.