diver's height above the surface of the water when diving can be modeled by the equation h=-16^2-8t+120 where h is the height above the water's surface measured in feet. How long will it take the diver to reach the surface of the water?

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Honey

Mathematics

30 January, 08:20

diver's height above the surface of the water when diving can be modeled by the equation h=-16^2-8t+120 where h is the height above the water's surface measured in feet. How long will it take the diver to reach the surface of the water?

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Lara Novak · Answer 1

The time it will take the diver to reach the surface of the water is:

2.5 seconds.

Step-by-step explanation:

Considering the provided equation, (I modified it a bit since I think you missed a variable t):

h = - 16t ^ 2-8t + 120

The time value is replaced by values from 0.1 seconds until the result is equal to zero, which means that it is at the same height from the water surface, however, since the iterations would be enough, so I will do the iterations every 0.5 seconds and you can see how the result, that is, the height, decreases:

h (0.5) = - 16 (0.5) ^ 2-8 (0.5) + 120 = 112 h (1) = - 16 (1) ^ 2-8 (1) + 120 = 96 h (1.5) = - 16 (1.5) ^ 2-8 (1.5) + 120 = 72 h (2) = - 16 (2) ^ 2-8 (2) + 120 = 40 h (2.5) = - 16 (2.5) ^ 2-8 (2.5) + 120 = 0

As you can see, when the time is equal to 2.5 seconds, the diver's height is equal to zero, so you can be sure that this time is the one spent in reaching the surface of the water.