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Jeriel launches a toy rocket from a platform. The height of the rocket in feet is given by h(t)=-16t^(2)+120 t+136 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

Jeriel launches a toy rocket from a platform. The height of the rocket in feet is given by h(t)=−16t2+120t+136 h(t)=-16 t^{2}+120 t+136 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. Jeriel launches a toy rocket from a platform. The height of the rocket in feet is given by h(t)=−16t2+120t+136 h(t)=-16 t^{2}+120 t+136 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 Quadratic Equation: Identify the quadratic equation that represents the height of the rocket.\newlineWe have the equation h(t)=−16t2+120t+136h(t) = -16t^2 + 120t + 136, which is a quadratic equation in the form of at2+bt+cat^2 + bt + c.\newlineHere, a=−16a = -16, b=120b = 120, and c=136c = 136.
  2. Calculate Time for Maximum Height: Calculate the time at which the rocket reaches its maximum height.\newlineThe time at which a quadratic equation reaches its maximum (or minimum) is given by the formula t=−b2at = -\frac{b}{2a}.\newlineSubstitute a=−16a = -16 and b=120b = 120 into the formula.\newlinet=−1202×−16t = -\frac{120}{2 \times -16}\newlinet=−120−32t = -\frac{120}{-32}\newlinet=3.75t = 3.75
  3. Check for Errors: Check the result for any mathematical errors.\newlineWe have calculated t=3.75t = 3.75 seconds. This is the time at which the rocket reaches its maximum height according to the vertex formula of a parabola.

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