The function h (t) = - 16t2 + 96t + 6 represents an object projected into the air from a cannon. The maximum height reached by the object is 150 feet. After how many seconds does the object reach its maximum height? 2 seconds 3 seconds 6 seconds 9 seconds

Question

Physics

Jeremiah Winters

19 May, 06:27

The function h (t) = - 16t2 + 96t + 6 represents an object projected into the air from a cannon. The maximum height reached by the object is 150 feet. After how many seconds does the object reach its maximum height? 2 seconds 3 seconds 6 seconds 9 seconds

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Answers (2)

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Elyse Brennan · Answer 1

3 seconds

Explanation:

Since h (t) represents the height and t represents the time, we can set the equation equal to 150 to find t.

-16t^2+96t+6=150

Subtract 150 from both sides to set the equation equal to 0, to find the solutions.

-16t^2+96t-144=0

Factor out - 16, because all of the terms are divisible by it.

-16 (t^2+6t+9) = 0

Now we can focus on the terms inside the parenthesis and factor it again.

t^2-6t+9=0

We need to find two value that can be multiplied to get 9 and added to get - 6.

-3 and - 3 works.

Thus, we get (x-3) (x-3).

Now solve for 0.

x-3=0

x=3

The object reaches its maximum height after 3 seconds.