1. Un proyectil se dispara con una velocidad inicial de 15 m/s formando un ángulo de 30 grados con respecto a la
horizontal, asumiendo una gravedad de m/s^2,
determinar :
a. El tiempo de subida y tiempo de bajada.
b. La altura máxima.
c. El alcance horizontal cuando la altura es máxima.
d. La velocidad con respecto al eje “Y” y “X”, cuando su altura es
máxima.
e. Distancia total recorrida.
f. Realice un bosquejo de la situación, señalando todos los valores
obtenidos.

Three different objects, all with different masses, are initially at rest at the bottom of a set of steps. each step is of uniform height . the mass of each object is a multiple of the base mass : object 1 has mass 4..00m , object 2 has mass 1..96m , and object 3 has mass . when the objects are at the bottom of the steps, define the total gravitational potential energy of the three-object system to be zero. if the objects are then relocated as shown, what is the new total potential energy of the system? each answer requires the numerical coefficient to an algebraic expression. each algebraic expression is given using some combination of the variables , , and , where is the acceleration due to gravity. enter only the numerical coefficient. (example: if the answer is 1..23mgd , just enter 1.23)

If state law mandates that elevators cannot accelerate more than 2.40 m/s2 or travel faster than 14.8 m/s , what is the minimum time in which an elevator can travel the 373 m from the ground floor to the observatory floor? ?

Amass m = 74 kg slides on a frictionless track that has a drop, followed by a loop-the-loop with radius r = 18.4 m and finally a flat straight section at the same height as the center of the loop (18.4 m off the ground). since the mass would not make it around the loop if released from the height of the top of the loop (do you know why? ) it must be released above the top of the loop-the-loop height. (assume the mass never leaves the smooth track at any point on its path.) 1. what is the minimum speed the block must have at the top of the loop to make it around the loop-the-loop without leaving the track? 2. what height above the ground must the mass begin to make it around the loop-the-loop? 3. if the mass has just enough speed to make it around the loop without leaving the track, what will its speed be at the bottom of the loop? 4. if the mass has just enough speed to make it around the loop without leaving the track, what is its speed at the final flat level (18.4 m off the ground)? 5. now a spring with spring constant k = 15600 n/m is used on the final flat surface to stop the mass. how far does the spring compress?