for the following question, use the function $h = -16t^2 + v_0t + h_0$, where $h$ is the height of the object after time $t$, $v_0$ is the initial velocity, and $h_0$ is the initial height.

an object is thrown upward from a height of $560\text{ ft}$ with an initial velocity of $32\text{ ft/s}$. how long will it take for the object to reach the ground?

Question

for the following question, use the function $h = -16t^2 + v_0t + h_0$, where $h$ is the height of the object after time $t$, $v_0$ is the initial velocity, and $h_0$ is the initial height.

an object is thrown upward from a height of $560\text{ ft}$ with an initial velocity of $32\text{ ft/s}$. how long will it take for the object to reach the ground?

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Polynomial Applications", "Solving Quadratic Equations", "Factoring Quadratic Equations" ], "new_concepts": [], "current_concepts": [ "Polynomial Applications", "Solving Quadratic Equations", "Factoring Quadratic Equations" ] } ## Identify given values and set up the equation Using the **Polynomial Applications** knowledge point $$ \begin{aligned} &h_0 = 560\text{ ft},\quad v_0 = 32\text{ ft/s},\quad h = 0\text{ ft}\ &-16t^2 + 32t + 560 = 0 \end{aligned} $$ ## Simplify the quadratic equation Using the **Solving Quadratic Equations** knowledge point $$ \begin{aligned} &-16(t^2 - 2t - 35) = 0\ &t^2 - 2t - 35 = 0 \end{aligned} $$ ## Factor the quadratic expression Using the **Factoring Quadratic Equations** knowledge point $$ \begin{aligned} &(t - 7)(t + 5) = 0 \end{aligned} $$ ## Solve for time and select the physical solution Using the **Solving Quadratic Equations** knowledge point $$ \begin{aligned} &t = 7\quad\text{or}\quad t = -5\ &t > 0 \implies t = 7\text{ seconds} \end{aligned} $$ An object is thrown upward from a height of 560 ft with an initial velocity of 32 ft / s. How long will it take for the object to reach the ground? 7 seconds { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Quadratic Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Identify given values and set up the equation

Simplify the quadratic equation

Factor the quadratic expression

Solve for time and select the physical solution

Answer: