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

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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) About Me  (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 (h%5B0%5D) with an initial velocity (v%5B0%5D):
h%28t%29+=+%281%2F2%29gt%5E2%2Bv%5B0%5Dt%2Bh%5B0%5D where g is the acceleration due to gravity, 32 ft/sec. sq. Making the appropriate substitutions:
h%28t%29+=+-16t%5E2%2B8t%2B24
To find the time the diver hits the water means to find the time (t) at which his height (h) is zero.
1) -16t%5E2%2B8t%2B24+=+0 Factor out -8.
-8%282t%5E2-t-3%29+=+0 Now factor the trinomial.
2t%5E2-t-3+=+%282t-3%29%28t%2B1%29=0 So...
2t-3%29+=+0 or t%2B1+=+0 and...
t+=+3%2F2 or t+=+-1 Discard the negative solution as the time will be a positive value.
t+=+3%2F2
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:
t+=+-b%2F2a and a = -16, b = 8.
t+=+%28-8%29%2F2%28-16%29
t+=+1%2F4seconds. Now substitute this value of t into equation 1) above and solve for h.
h%281%2F4%29+=+-16%281%2F4%29%5E2%2B8%281%2F4%29%2B24
h%281%2F4%29+=+-16%281%2F16%29%2B%288%2F4%29%2B24
h%281%2F4%29+=+-1%2B2%2B24
h%281%2F4%29+=+25feet.
The diver attains a maximum height of 25 feet above the water.