An object is thrown horizontally off a cliff with an initial velocity of 5.0 meters per second. the object strikes the ground 3.0 seconds later. what is the vertical speed of the object as it reaches the ground? [neglect friction.]

The acceleration of gravity is 9.8 m/s².  This simply means that when anything falls, its downward speed keeps increasing, and it falls 9.8 m/s faster every second than it fell 1 second earlier.

After 3 seconds of falling, the object is falling at (3 x 9.8 m/s) = 29.4 m/s faster than at the beginning of the 3 seconds.  If it had no vertical speed at the beginning of the 3 seconds, then THAT's its speed after 3 seconds . . . . . 29.4 m/s downward.

As far as being thrown horizontally off the cliff . . . that has no effect on it vertical speed.  Horizontally, it doesn't matter whether it rolls gently over the edge, or somebody throws it horizontally, or it gets shot horizontally out of a high power rifle.  It hits the ground at the same time and with the same speed in every case.

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