A regulation volleyball court is L = 18.0 m long and a regulation volleyball net is d = 2.43 m high. A volleyball player strikes the ball a height h = 1.76 m directly above the back line, and the ball's initial velocity makes an angle q = 55° with respect to the ground.

From this information, I have been able to determine: 1) the initial speed the ball must be hit so that it just barely makes it over the net (9.96 m/s), 2) the maximum height above the court reached by the ball in that case (5.15 m), 3) the initial speed the ball must be hit so that it lands directly on the opponent's back line (13.3 m/s), and 4) the max. height reached by the ball in that case (7.77 m).

Now it says: "In volleyball, it is often advantageous to serve the ball as hard as possible. If you want the ball to land in the opponent's court, however, there is an upper limit on the initial ball speed for a given contact point. At this maximum speed, the ball just barely makes it over the net and then just barely lands in bounds on the back line of the opponent's court. For the contact point given in the previous problems, what is this maximum initial speed?"

What equation can I use to solve this? I've tried a couple of different ways before, and nothing seems to be working.

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  1. Use the vertical displacement equation to find the time of flight in terms of initial velocity. Then use the horizontal displacement equation with that expression for time to find the initial velocity.

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