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A rocket is launched in the air. Its height in feet is given by h=-16t^(2)+96 t where t represents the time in seconds after launch. How many seconds have gone by when the rocket is at its highest point? Answer: seconds

A rocket is launched in the air. Its height in feet is given by h=−16t2+96t h=-16 t^{2}+96 t where t t represents the time in seconds after launch. How many seconds have gone by when the rocket is at its highest point?\newlineAnswer: seconds

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Q. A rocket is launched in the air. Its height in feet is given by h=−16t2+96t h=-16 t^{2}+96 t where t t represents the time in seconds after launch. How many seconds have gone by when the rocket is at its highest point?\newlineAnswer: seconds
  1. Identify Constants: Identify the values of aa, bb, and cc in the quadratic equation.\newlineThe given equation is h=−16t2+96th=-16t^{2}+96t. This is a quadratic equation in the form of at2+bt+cat^2 + bt + c, where aa, bb, and cc are constants.\newlineHere, a=−16a = -16, b=96b = 96, and cc is not present, which means bb11.
  2. Find Vertex: Find the tt-coordinate of the vertex of the parabola.\newlineThe tt-coordinate of the vertex of a parabola given by the equation at2+bt+cat^2 + bt + c is found using the formula t=−b2at = -\frac{b}{2a}.\newlineSubstitute a=−16a = -16 and b=96b = 96 into the formula.\newlinet=−962∗(−16)t = -\frac{96}{2*(-16)}\newlinet=−96−32t = -\frac{96}{-32}\newlinet=3t = 3
  3. Determine Max Height: Determine the time at which the rocket reaches its maximum height.\newlineWe have found that the tt-coordinate of the vertex is t=3t = 3 seconds. This is the time at which the rocket will be at its highest point.

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