Recall from the previous two pages that the horizontal and vertical positions/displacements are calculated indepedent of each other and that the velocity calculation can tell the direction of motion.
Some motions are not ONLY vertical or ONLY horizontal. These motion occur at an initial angle. They can be described as having some amount of initial velocity in the vertical direction and some initial velocity in the horizontal direction.
When a problem is given like this, then it is creating two problems. One that needs to be solved using only the vertical givens, like the problem on page 1 of this chapter. And another problem that is solved like the ones on page 2 of this chapter.
A ball is thrown off the top of a cliff with an initial vertical velocity if 4.00 m/s upwards and with a horizontal velocity of 6.00 m/s. Neglect air resistance. Vertically the ball experiences the acceleration due to gravity. Horizontally the ball is moving at a constant velocity. What is the position of the ball after 3.00 seconds?