The veloctiy in the Ydirection is going to be Vy=Vo*sin(theta). Since gravity(G) is the only force acting on the ball, it will be deaccelerating in the Y direction and the rate of gravity, which is 9.81 m/s squared.
The velocity in the X direction is Vx=Vo*cos(theta).
The time that is takes the ball to reach its maximum height will be when the velocity in the Y direction is 0. You can find time=t by dividing your inital velocity by |G|.
For finding the maximum height the basketball will reach, we will use the displacement formula. The displacement formula for projectile motion is d=V*t + 1/2*a*t*t. Once we find the time it takes the ball to reach this heigh, we can find what the height will be.
Since the flight of our projectile is symmetric, we can find how far it has traveled in respect to the ground by mutilplying the velocity in the x direction by the time it take to reach this heigh. The time it will then take it to travel from the maximum height to the basket can be viewed as a car driving off a cliff. If the max height is 5m and the basketball hoop is 3m high, then we can figure out how far it will take the ball to travel 2m in the y direction, which is 2/10=.2. Knowing the time is will take the ball to reach the necessary height in the y direction, we can then figure out how far away the max height must be from the basket by multiplying the velocity in the x direction by the time t=.2.
Basketball players, of course, don't need to work out how fast they should throw the ball and at what angle with a piece of paper and pencil for every shot, but intuitivly, that is exactly what they do.