a ball is thrown into the air with an upward velocity of 80 feet per second. the function $h = -16t^2 + 80t$ models the height $h$, in feet, of the ball at time $t$, in seconds. when will the ball reach the ground?

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Question

a ball is thrown into the air with an upward velocity of 80 feet per second. the function \$h = -16t^2 + 80t\$ models the height \$h\$, in feet, of the ball at time \$t\$, in seconds. when will the ball reach the ground?

after 3 seconds
after 4 seconds
after 5 seconds
after 6 seconds

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" ] } ## Set height to zero for ground level $$ h = 0 $$ ## Solve the quadratic equation for time $$ \begin{aligned} -16t^2 + 80t &= 0 \ -16t(t - 5) &= 0 \end{aligned} $$ ## Identify the non-zero time solution $$ \begin{aligned} t &= 0 \quad \text{or} \quad t = 5 \ t &= 5 \text{ seconds} \end{aligned} $$

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{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Zeros of Quadratic Functions" ] }

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QUESTION IMAGE

Question

Explanation:

Set height to zero for ground level

Solve the quadratic equation for time

Identify the non-zero time solution

Answer: