Europa, a satellite of jupiter, is believed to have a liquid ocean of water (with a possibility of life) beneath its icy surface. in planning a future mission to europa, what is the fastest that an astronaut with legs of length 0.67 m could walk on the surface of europa? europa is 3100 km in diameter and has a mass of 4.8×1022kg.

maximum speed  = 0.94490 Nm/kg

Explanation:

Given data

length = 0.67 m

diameter = 3100 km 3100000 m

mass = 4.8×10^22 kg

to find  out

maximum speed

solution

we will use here gravitational constant equation for find acceleration due to gravity at europa i.e

g = GM/r²

g = 6.67 × 10^(-11) ×  4.8×10^22 / (3100000/2)²

g = 1.332611862 Nm²/kg-m

so maximum speed will be √(gr)

maximum speed  = √( 1.332611862 × 0.67 )

maximum speed  = 0.94490 Nm/kg

photocells convert light energy to electricity

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.