a soccer ball kicked from the ground with an initial velocity of 32 ft/s is given by the function $h(t) = -16t^2 + 32t$. when is the soccer ball moving through the air?

$\{t \mid -2

Question

a soccer ball kicked from the ground with an initial velocity of 32 ft/s is given by the function $h(t) = -16t^2 + 32t$. when is the soccer ball moving through the air?

$\{t \mid -2 < t < 2\}$
$\{t \mid -4 < t < 4\}$
$\{t \mid 0 < t < 2\}$
$\{t \mid 0 < t < 4\}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Zeros of Quadratic Functions", "Projectile Motion Modeling" ], "new_concepts": [], "current_concepts": [ "Zeros of Quadratic Functions", "Projectile Motion Modeling", "Function Inequalities" ] } ## Find the times when the ball is on the ground $$ \begin{aligned} h(t) &= 0 \ -16t^2 + 32t &= 0 \ -16t(t - 2) &= 0 \ t = 0 \quad &\text{or} \quad t = 2 \end{aligned} $$ ## Determine the interval when the ball is in the air $$ \begin{aligned} h(t) &> 0 \ -16t(t - 2) &> 0 \ 0 < t &< 2 \end{aligned} $$

(A) $\{t \mid -2 < t < 2\}$

(B) $\{t \mid -4 < t < 4\}$

(C) $\{t \mid 0 < t < 2\}$

(D) $\{t \mid 0 < t < 4\}$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Projectile Motion Modeling" ] }

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QUESTION IMAGE

Question

Explanation:

Find the times when the ball is on the ground

Determine the interval when the ball is in the air

Answer: