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A large explosion causes wood and metal debris to rise vertically into the air with an initial velocity of 96 feet per second. The quadratic function h(t)=96t−16t2 gives the height h (in feet) of the debris at time t (in seconds) after the explosion. How many seconds will it take before the debris falls back to the ground? Do not include units in your answer.

Answer :

Answer:

6

Step-by-step explanation:

The height of the debris after t seconds is given by the following equation:

[tex]h(t) = 96t - 16t^{2}[/tex]

How many seconds will it take before the debris falls back to the ground?

This is t for which

[tex]h(t) = 0[/tex]

So

[tex]96t - 16t^{2} = 0[/tex]

[tex]16t(6 - t) = 0[/tex]

[tex]16t = 0[/tex] or [tex]6 - t = 0[/tex]

[tex]t = 0[/tex] or [tex]t = 6[/tex]

The debris start at the ground(t = 0), go up, and come back to the ground at t = 6s.

So it takes 6 seconds for the debris to fall back to the ground.

fichoh

Using the quadratic function given, the debris would fall back to the ground at height, h = 0 ; hence, the time taken, t will be 6

Given the quadratic function :

  • h(t) = - 16t² + 96t

The debris would fall back to the ground at height, h = 0 :

-16t² + 96t = 0

-t² + 6t = 0

t(-t + 6) = 0

(-t + 6 = 0) or t = 0

-t + 6 = 0

6 = t

Hence, the debris will fall back to the ground after 6 seconds.

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