a toy rocket is launched from a $2.8\text{ m}$ high platform in such a way that its height, $h$ (in meters), after $t$ seconds is given by the equation $h = -4.9t^2 + 18.9t + 2.8$. how long will it take for the rocket to hit the ground?

the toy rocket will hit the ground after seconds.
(type an integer or a decimal.)

Question

a toy rocket is launched from a $2.8\text{ m}$ high platform in such a way that its height, $h$ (in meters), after $t$ seconds is given by the equation $h = -4.9t^2 + 18.9t + 2.8$. how long will it take for the rocket to hit the ground?

the toy rocket will hit the ground after   seconds.
(type an integer or a decimal.)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Quadratic Equations", "Quadratic Formula Application" ], "new_concepts": [], "current_concepts": [ "Quadratic Equations", "Quadratic Formula Application", "Quadratic Formula" ] } ## Set the height equation to zero $$ -4.9t^2 + 18.9t + 2.8 = 0 $$ ## Apply the quadratic formula to solve for t $$ \begin{aligned} t &= \frac{-18.9 \pm \sqrt{18.9^2 - 4(-4.9)(2.8)}}{2(-4.9)} \ t &= \frac{-18.9 \pm \sqrt{357.21 + 54.88}}{-9.8} \ t &= \frac{-18.9 \pm \sqrt{412.09}}{-9.8} \ t &= \frac{-18.9 \pm 20.3}{-9.8} \end{aligned} $$ ## Calculate the physically valid time $$ \begin{aligned} t_1 &= \frac{-18.9 + 20.3}{-9.8} = \frac{1.4}{-9.8} \approx -0.143 \ t_2 &= \frac{-18.9 - 20.3}{-9.8} = \frac{-39.2}{-9.8} = 4 \end{aligned} $$ A toy rocket is launched from a 2.8 m high platform in such a way that its height, h (in meters), after t seconds is given by the equation $h = -4.9t^2 + 18.9t + 2.8$. How long will it take for the rocket to hit the ground? The toy rocket will hit the ground after 4 seconds. (Type an integer or a decimal.) { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Quadratic Formula Application" ] }

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Question

Explanation:

Set the height equation to zero

Apply the quadratic formula to solve for t

Calculate the physically valid time

Answer: