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H(t) = -16t² + 8t + 200, please solve in height to time.

User Strocknar
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Final answer:

To find the time (t) when h(t) = -16t² + 8t + 200, we use the quadratic formula after rearranging the terms to zero. After substituting the known values into the quadratic formula, we solve to find t ≈ 3.79 seconds as the physical solution since time cannot be negative.

Step-by-step explanation:

To solve the quadratic equation h(t) = -16t² + 8t + 200 for time (t), we first rearrange the terms to set the equation to zero:

0 = -16t² + 8t + 200

We then use the quadratic formula which is given by:

t = −(b ± √(b² − 4ac)) / (2a)

Where, in our equation, a = -16, b = 8, and c = 200. Substituting these values into the quadratic formula, we get:

t = −(8 ± √(8² − 4(-16)(200))) / (2(-16))

Calculating under the square root:

t = −(8 ± √(64 + 12800)) / (-32)

t = −(8 ± √(12864)) / (-32)

After further simplification:

t = −(8 ± 113.4) / (-32)

We end up with two possible solutions for time:

  • t = (8 + 113.4) / 32
  • t = (8 - 113.4) / 32

Since time cannot be negative, we discard the solution that gives us a negative time, resulting in:

t = 121.4 / 32 ≈ 3.79 seconds

User Georg Zimmer
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