the quadratic model $f(x) = -5x^2 + 200$ represents the approximate height, in meters, of a ball $x$ seconds after being dropped. the ball is 50 meters from the ground after about how many seconds?

2.45
3.16
5.48
7.07

Question

the quadratic model $f(x) = -5x^2 + 200$ represents the approximate height, in meters, of a ball $x$ seconds after being dropped. the ball is 50 meters from the ground after about how many seconds?

2.45
3.16
5.48
7.07

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Projectile Motion Modeling" ], "new_concepts": [], "current_concepts": [ "Projectile Motion Modeling", "Quadratic Modeling" ] } ## Set up the quadratic equation $$ \begin{aligned} f(x) &= -5x^2 + 200 \ 50 &= -5x^2 + 200 \end{aligned} $$ ## Solve for x $$ \begin{aligned} -150 &= -5x^2 \ x^2 &= 30 \ x &= \sqrt{30} \approx 5.477 \end{aligned} $$ ## Match with the closest option $$ x \approx 5.48 $$

(A) 2.45

(B) 3.16

(C) 5.48

(D) 7.07

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

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Question

Explanation:

Set up the quadratic equation

Solve for x

Match with the closest option

Answer: