dynamics
projectiles
9. neil armstrong struck a golf ball from the first tee at lunar golf and country club at a velocity of $48\text{ m/s}$ at an angle of $40^\circ$ to the horizontal. on the moon, $a_{\text{gravity}} = -1.6\text{ m/s}^2$. how far will the ball travel horizontally?

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": true, "concepts_used": [ "Projectile Motion", "Lunar Gravity" ], "new_concepts": [], "current_concepts": [ "Projectile Motion", "Lunar Gravity", "Kinematics" ] } ## Resolve initial velocity components Using the **Projectile Motion** knowledge point $$ \begin{aligned} v_{0x} &= v_0 \cos(\theta) = 48 \cos(40^\circ) \approx 36.77\text{ m/s} \ v_{0y} &= v_0 \sin(\theta) = 48 \sin(40^\circ) \approx 30.85\text{ m/s} \end{aligned} $$ ## Calculate time of flight Using the **Lunar Gravity** and **Projectile Motion** knowledge points $$ \begin{aligned} &a_y = -1.6\text{ m/s}^2 \ &t_{\text{up}} = \frac{0 - v_{0y}}{a_y} = \frac{-30.85}{-1.6} \approx 19.28\text{ s} \ &t_{\text{total}} = 2 \times t_{\text{up}} \approx 38.56\text{ s} \end{aligned} $$ ## Calculate horizontal displacement Using the **Projectile Motion** knowledge point $$ \begin{aligned} d_x &= v_{0x} \times t_{\text{total}} \ d_x &\approx 36.77 \times 38.56 \approx 1418\text{ m} \end{aligned} $$ The golf ball will travel approximately $1.4 \times 10^3\text{ m}$ (or $1418\text{ m}$) horizontally. { "elements": [ { "type": "functiongraph", "params": [ { "js": "30.85*(x/36.77) - 0.5*1.6*(x/36.77)*(x/36.77)", "latex": "y = v_{0y}\left(\frac{x}{v_{0x}}\ ight) - \frac{1}{2}g_{\text{moon}}\left(\frac{x}{v_{0x}}\ ight)^2" }, 0, 1418 ], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 3, "name": "Trajectory", "withLabel": true } }, { "type": "point", "params": [[0, 0]], "properties": { "name": "Tee", "color": "#5583F2", "strokeColor": "#5583F2", "withLabel": true } }, { "type": "point", "params": [[1418, 0]], "properties": { "name": "Landing", "color": "#F2557F", "strokeColor": "#F2557F", "withLabel": true } } ], "timestamps": [0.5, 1.0] } { "subject": "Natural Science", "question_type": "Word Problem", "knowledge_point": [ "Natural Science", "Physics", "Projectile Motion" ] }

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Explanation:

Resolve initial velocity components

Calculate time of flight

Calculate horizontal displacement

Answer: