6. $v = 18\text{ m/s}$
$\theta = 35^\circ$
$g = 9.81$
$x = ?$
$y = ?$
$t_f = ?$
$v_x = 14.71$
$v_y = 10.32$
$t_{\text{total}} = 2.1\text{ seg}$

7) $f = 45\frac{\text{rev}}{\text{min}} \left(\frac{1\text{ min}}{60\text{ s}}\
ight) = 0.75\frac{\text{rev}}{\text{s}}$
$r = 0.8\text{ m}$
$w = 4.71\frac{\text{rad}}{\text{s}}$
$v = ?$

8) $g = -1.62\text{ m/s}^2$
$y = -40\text{ m}$
$t = ?$
$v_f = ?$
$v_0 = 0\text{ m/s}$

Question

6. $v = 18\text{ m/s}$
$\theta = 35^\circ$
$g = 9.81$
$x = ?$
$y = ?$
$t_f = ?$
$v_x = 14.71$
$v_y = 10.32$
$t_{\text{total}} = 2.1\text{ seg}$

7) $f = 45\frac{\text{rev}}{\text{min}} \left(\frac{1\text{ min}}{60\text{ s}}\
ight) = 0.75\frac{\text{rev}}{\text{s}}$
$r = 0.8\text{ m}$
$w = 4.71\frac{\text{rad}}{\text{s}}$
$v = ?$

8) $g = -1.62\text{ m/s}^2$
$y = -40\text{ m}$
$t = ?$
$v_f = ?$
$v_0 = 0\text{ m/s}$

Accepted Answer

{ "quality": "clear", "question_count": 3, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Movimiento de proyectiles", "Velocidad inicial", "Tiempo de vuelo" ], "new_concepts": [ "Movimiento circular uniforme", "Caída libre" ], "current_concepts": [ "Movimiento de proyectiles", "Velocidad inicial", "Tiempo de vuelo", "Movimiento circular uniforme", "Caída libre" ] } ## Resolver el problema 6 (Movimiento de proyectiles) $$ \begin{aligned} v_0 &= 18\text{ m/s},\quad \theta = 35^\circ,\quad g = 9.81\text{ m/s}^2\ v_x &= v_0 \cos\theta = 18 \cos(35^\circ) \approx 14.74\text{ m/s}\ v_{0y} &= v_0 \sin\theta = 18 \sin(35^\circ) \approx 10.32\text{ m/s}\ t_{\text{subida}} &= \frac{v_{0y}}{g} = \frac{10.32}{9.81} \approx 1.05\text{ s}\ t_{\text{total}} &= 2 \times t_{\text{subida}} \approx 2.10\text{ s}\ x &= v_x t_{\text{total}} = 14.74 \times 2.10 \approx 30.95\text{ m} \end{aligned} $$ ## Resolver el problema 7 (Movimiento circular) $$ \begin{aligned} f &= 45\text{ rev/min} = \frac{45}{60}\text{ rev/s} = 0.75\text{ Hz}\ \omega &= 2\pi f = 2\pi(0.75) \approx 4.71\text{ rad/s}\ R &= 0.8\text{ m}\ v &= \omega R = 4.71 \times 0.8 \approx 3.77\text{ m/s} \end{aligned} $$ ## Resolver el problema 8 (Caída libre en la Luna) $$ \begin{aligned} g &= -1.62\text{ m/s}^2,\quad y = -40\text{ m},\quad v_0 = 0\text{ m/s}\ t &= \sqrt{\frac{2y}{g}} = \sqrt{\frac{2(-40)}{-1.62}} \approx 7.03\text{ s}\ v_f &= v_0 + gt = 0 + (-1.62)(7.03) \approx -11.39\text{ m/s} \end{aligned} $$ ## Pregunta 6 * **Velocidad horizontal ($v_x$):** $14.74\text{ m/s}$ * **Velocidad vertical inicial ($v_{0y}$):** $10.32\text{ m/s}$ * **Tiempo de vuelo total ($t_{\text{total}}$):** $2.10\text{ s}$ * **Alcance horizontal ($x$):** $30.95\text{ m}$ ## Pregunta 7 * **Frecuencia ($f$):** $0.75\text{ rev/s}$ * **Velocidad angular ($\omega$):** $4.71\text{ rad/s}$ * **Velocidad lineal ($v$):** $3.77\text{ m/s}$ ## Pregunta 8 * **Tiempo de caída ($t$):** $7.03\text{ s}$ * **Velocidad final ($v_f$):** $-11.39\text{ m/s}$ { "subject": "Natural Science", "question_type": "Multi-part", "knowledge_point": [ "Natural Science", "Physics", "Kinematics" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Resolver el problema 6 (Movimiento de proyectiles)

Resolver el problema 7 (Movimiento circular)

Resolver el problema 8 (Caída libre en la Luna)

Answer:

Pregunta 6

Pregunta 7

Pregunta 8