Hello, anybody if you
a swimmer runs horizontally off a diving board with a speed of 3.62m/s and hits the water a horizontal distance of 1.68m from the end of the board. (a.) how high above the water was the diving board? (b) if the swimmer runs off the board with a reduced speed, does it take more, less, or the same time to reach the water?
you! : )

This is called "projectile motion".  The projectile can be a baseball,
a bullet, a golf ball, or a rock that somebody tossed.  In this story, 
the swimmer is the projectile.

In projectile motion, the projectile is moving part horizontally and part
vertically at the same time.  The thing to remember about this kind of
motion is:  The horizontal motion doesn't change, but the vertical motion
changes because of gravity ... just like an apple that fell from a tree.

The swimmer runs straight horizontally off the diving board.  His horizontal speed is 3.62 m/s.  He hits the water  1.68 m from the end of the board.  How long did it take him to go that far ?

       Time  =  (distance) / (speed)

                 =  (1.68 m) / (3.62 m/s)

                 =  (1.68 / 3.62)  seconds

                 =          0.464 second .

(a).
How high above the water was the diving board ?
Well, the swimmer was falling for 0.464 second .
The height is whatever it takes 0.464 second to fall.

           Height  = (1/2) x (acceleration of gravity) x (time)²

                        = (1/2) x      (9.8 m/s²)                  x (0.464 sec)²

                        =        (4.9 m/s²)                x             (0.2153 sec²)

                        =              (4.9  x  0.2153)     meters

                        =                    1.055  meters .  

(b). 
If the swimmer runs off the board slower, his horizontal speed is
lower.  That only affects how far out in front of the board he'll be
when he hits the water.  But his horizontal speed has no effect
on how long it takes him to fall to the water.  That's his vertical
speed, and it only depends on gravity. 
No matter how fast or slow he runs off the board, or if he just
stands there at the end and leans over until he falls, it takes him
the same time to reach the water in every case.