question 2 (2 points)

on mars, if you hit a baseball, the height of the ball at time $t$ would be modelled by the quadratic function $h(t) = -1.85t^2 + 20t + 1$, where $t$ is in seconds and $h(t)$ is in metres.

when will the ball hit the ground?

10.9 s
23.5 s
18.6 s
0.8 s

Question

question 2 (2 points)

on mars, if you hit a baseball, the height of the ball at time $t$ would be modelled by the quadratic function $h(t) = -1.85t^2 + 20t + 1$, where $t$ is in seconds and $h(t)$ is in metres.

when will the ball hit the ground?

10.9 s
23.5 s
18.6 s
0.8 s

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Quadratic Relations", "Finding Roots" ], "new_concepts": [ "Quadratic Word Problems" ], "current_concepts": [ "Quadratic Relations", "Finding Roots", "Quadratic Word Problems" ] } ## Set the height function to zero $$ -1.85t^2 + 20t + 1 = 0 $$ ## Apply the quadratic formula $$ \begin{aligned} t &= \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \ t &= \frac{-20 \pm \sqrt{20^2 - 4(-1.85)(1)}}{2(-1.85)} \ t &= \frac{-20 \pm \sqrt{400 + 7.4}}{-3.7} \ t &= \frac{-20 \pm \sqrt{407.4}}{-3.7} \end{aligned} $$ ## Calculate the positive time value $$ \begin{aligned} t &\approx \frac{-20 \pm 20.184}{-3.7} \ t_1 &\approx \frac{-20 - 20.184}{-3.7} \approx 10.86\text{ s} \ t_2 &\approx \frac{-20 + 20.184}{-3.7} \approx -0.05\text{ s} \end{aligned} $$

(A) 10.9 s

(B) 23.5 s

(C) 18.6 s

(D) 0.8 s

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Quadratic Word Problems" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Set the height function to zero

Apply the quadratic formula

Calculate the positive time value

Answer: