8) If a swimmer runs off a diving board with a velocity of 7.1m/s, if the swimmer hits the pool 4m away from the diving board, how long did it take for the swimmer to hit the water?

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.