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.

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 :

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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Step-by-step explanation:

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

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

This is t for which

So

or

or

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.

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step-by-step explanation: