En la tierra un volcán puede expulsar rocas verticalmente hasta una altura máxima h. a) ¿a qué altura (en términos de h) llegarían es- tas rocas si un volcán en marte las expulsara con la misma velocidad inicial? la aceleración debida a la gravedad en marte es de 3.71 m> s2, y se puede despreciar la resistencia del aire en ambos planetas. b) si en la tierra las rocas están en el aire un tiempo t, ¿por cuánto tiempo (en términos de t) estarán en el aire en marte?

A) 2.64 H

The maximum height that the expelled rock can reach can be found by using the equation:

where

v = 0 is the velocity at the maximum height

u is the initial velocity

g is the acceleration of gravity

d is the maximum height

Solving for d,

We see that the maximum heigth is inversely proportional to g. On the Earth,

and

So we can write:

where H' is the maximum height reached on Mars, and is the acceleration of gravity on Mars. Solving for H',

B) 2.64T

The time after which the rock reaches the maximum height can be found by using

where

v = 0 is the velocity at the maximum height

u is the initial velocity

Solving for t,

The total time of the motion is twice this value, so:

So we see that it is inversely proportional to g.

On the Earth, t = T. So we can write:

where T' is the total time of the motion on Mars. Solving for T',

c) up is the direction the magnetic force is acting on the charge.

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

where is unknown. because the position is parabolic, there is symmetry about the midpoint at , and we know that

so that the position function is

which means the velocity is

then the total distance traveled is

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at and ends at , so its displacement is 0.