benjamin threw a rock straight up from a cliff that was 36 ft above the water. if the height of the rock $h$, in feet, after $t$ seconds is given by the equation $h = -16t^2 + 36t + 36$, how long will it take for the rock to hit the water?

the rock will hit the water in seconds.

Question

benjamin threw a rock straight up from a cliff that was 36 ft above the water. if the height of the rock \$h\$, in feet, after \$t\$ seconds is given by the equation \$h = -16t^2 + 36t + 36\$, how long will it take for the rock to hit the water?

the rock will hit the water in seconds.

the rock will hit the water in   seconds.

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" ], "new_concepts": [ "Projectile Motion Equations" ], "current_concepts": [ "Quadratic Equations", "Quadratic Formula", "Projectile Motion Equations" ] } ## Set the height equation to zero $$ -16t^2 + 36t + 36 = 0 $$ ## Simplify the quadratic equation $$ \begin{aligned} -4(4t^2 - 9t - 9) &= 0 \ 4t^2 - 9t - 9 &= 0 \end{aligned} $$ ## Solve for t using factoring $$ \begin{aligned} (4t + 3)(t - 3) &= 0 \ t = -\frac{3}{4} \quad &\text{or} \quad t = 3 \end{aligned} $$ Since time $t$ must be positive: $$ t = 3 $$ Benjamin threw a rock straight up from a cliff that was 36 ft above the water. If the height of the rock h, in feet, after t seconds is given by the equation $h = -16t^2 + 36t + 36$, how long will it take for the rock to hit the water? The rock will hit the water in 3 seconds. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Quadratic Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Set the height equation to zero

Simplify the quadratic equation

Solve for t using factoring

Answer: