SOLUTION: A swimmer is about to dive into a pool from the end of a diving board that is 24 feet above the waters surface. if he springs up from the board at a speed of 8 feet per second, whe

Question 194403: A swimmer is about to dive into a pool from the end of a diving board that is 24 feet above the waters surface. if he springs up from the board at a speed of 8 feet per second, when will he hit the water? what will be his maximum height above the water?
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
You can use the equation for the height of an object propelled upwards from an initial height () with an initial velocity ():
where g is the acceleration due to gravity, 32 ft/sec. sq. Making the appropriate substitutions:

To find the time the diver hits the water means to find the time (t) at which his height (h) is zero.
1) Factor out -8.
Now factor the trinomial.
= So...
or and...
or Discard the negative solution as the time will be a positive value.

The diver will hit the water in 1.5 seconds.
His maximum height can be found by finding the coordinates of the vertex (a maximum) of the downward-opening parabola represented by the quadratic equation.
The t-value is given by:
and a = -16, b = 8.

seconds. Now substitute this value of t into equation 1) above and solve for h.

feet.
The diver attains a maximum height of 25 feet above the water.

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