part b: short answer (11 marks)

wr1. a stone is thrown horizontally with a speed of $8.00\text{ m/s}$ from the top of a cliff that is $113\text{ m}$ high. determine how far from the base of the cliff the stone will land. (3 marks) show all work and give the answer in significant digits.

Question

part b: short answer (11 marks)

wr1. a stone is thrown horizontally with a speed of $8.00\text{ m/s}$ from the top of a cliff that is $113\text{ m}$ high. determine how far from the base of the cliff the stone will land. (3 marks) show all work and give the answer in significant digits.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": true, "concepts_used": [ "Uniform Motion", "Kinematic Equations" ], "new_concepts": [ "Projectile Motion", "Horizontal Projectile" ], "current_concepts": [ "Uniform Motion", "Kinematic Equations", "Projectile Motion" ] } ## Identify given values and target unknown Using the *Kinematic Equations* and *Uniform Motion* knowledge points $$ \begin{aligned} &v_{ix} = 8.00\text{ m/s},\quad v_{iy} = 0\text{ m/s}\ &d_y = -113\text{ m},\quad a_y = -9.81\text{ m/s}^2\ &\text{Target: } d_x \end{aligned} $$ ## Calculate time of flight Using the *Kinematic Equations* knowledge point $$ \begin{aligned} &d_y = v_{iy}t + \frac{1}{2}a_yt^2\ &-113 = 0 + \frac{1}{2}(-9.81)t^2\ &t^2 = \frac{226}{9.81} \approx 23.0377\ &t \approx 4.80\text{ s} \end{aligned} $$ ## Calculate horizontal distance Using the *Uniform Motion* knowledge point $$ \begin{aligned} &d_x = v_{ix}t\ &d_x = 8.00 \times 4.7997 \approx 38.4\text{ m} \end{aligned} $$ $38.4\text{ m}$ { "elements": [ { "type": "point", "params": [[0, 5]], "properties": { "name": "Cliff Top", "color": "#8C55F2", "size": 4, "withLabel": true } }, { "type": "segment", "params": [[0, 0], [0, 5]], "properties": { "strokeColor": "#583C87", "strokeWidth": 3, "name": "Cliff" } }, { "type": "segment", "params": [[0, 0], [8, 0]], "properties": { "strokeColor": "#5583F2", "strokeWidth": 2, "name": "Ground" } }, { "type": "curve", "params": [ { "x": { "js": "t", "latex": "t" }, "y": { "js": "5 - (5/36)*t*t", "latex": "5 - \frac{5}{36}t^2" } }, 0, 6 ], "properties": { "strokeColor": "#F2557F", "strokeWidth": 3, "dash": 2 } }, { "type": "point", "params": [[6, 0]], "properties": { "name": "Landing Point", "color": "#F2557F", "size": 4, "withLabel": true } }, { "type": "arrow", "params": [[0, 5], [2, 5]], "properties": { "strokeColor": "#55DDF2", "strokeWidth": 2, "name": "v_x" } } ] } { "subject": "Natural Science", "question_type": "Free Response", "knowledge_point": [ "Natural Science", "Physics", "Projectile Motion" ] }

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Question

Explanation:

Identify given values and target unknown

Calculate time of flight

Calculate horizontal distance

Answer: