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An object is dropped from a height of 1600 feet off the ground. The height h of the object after t seconds can be found using the equation h=1600−16t^2. When will the object reach the ground?

(Solve by factoring & Show work.)

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Answer:

The object reaches the ground after 10 seconds.

Explanation:

The height h (in feet) of the object after t seconds is modeled by the equation:


h=1600-16t^2

And we want to determine the time at which the object reaches the ground.

If it reaches the ground, its height h above ground will be 0. So:


0=1600-16t^2

We can solve for t. First, simplify by dividing both sides by 16:


0=100-t^2

Factor using the difference of two squares pattern:


0=(10-t)(10+t)

Zero Product Property:


10-t=0\text{ or } 10+t=0

Solve for each case:


t=10\text{ or } t=-10

Time cannot be negative. Thus, our only solution is:


t=10\text{ seconds}

The object reaches the ground after 10 seconds.

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