QUESTION 1: EPICYCLIC GEAR AND GEAR TRAINS An epicyclic gear train has a sun wheel with 24 teeth, and two planetary wheels of 46 teeth each, The latter mesh with the internal teeth of a fixed annulus with 116 teeth. The input shaft, carrying the sun wheel, transmits \( 4,5 \mathrm{~kW} \) at \( 280 \mathrm{r} / \mathrm{min} \). The output shaft is connected to an arm L that carries the planetary wheels. Calculate the speed of the output shaft.

f Steve throws the football 50 meters in 3 seconds, what is the average speed of the football? (nearest hundredth) If it takes Ashley 3 seconds to run from the batters box to first base at an average spe of 6.5 meters per second, what is the distance she covers in that time? \( \begin{array}{l}\text { Bart ran } 5000 \text { meters from the cops and an average speed of } 8 \text { meters/second before } \\ \text { he got caught. How long did he run? }\end{array} \)

Sloths are known for being slow. An average tree sloth moves at a speed of \( 0.743 \mathrm{~m} / \mathrm{s} \). T the nearest second, how long does it take a sloth to travel 22.3 m at this speed?

What is the dot product of vector \( j \) with a magnitude of 4 and a direction of \( 30^{\circ} \) and vector k with a magnitude of 10 and a direction of \( 15^{\circ} \) ? (Round your answer to the nearest tenth.)

2) ¿Qué aceleración adquiere si se le aplica el doble de fuerza que en el punto anterior? ¿Y si se le aplica el triple? Hacé los cálculos aplicando la fórmula, luego justificalo a través del enunciado de la Segunda Ley.

Una pesante maniglia in ottone ha una massa di \( 3,40 \mathrm{~kg} \). Quale volume in \( \mathrm{cm}^{3} \) occupa la maniglia? La densità dell'ottone è \( 8,40 \cdot 10^{3} \mathrm{~kg} / \mathrm{m}^{3} \).