Answer:
13.7m
Explanation:
Since there's no external force acting on the astronaut or the satellite, the momentum must be conserved before and after the push. Since both are at rest before, momentum is 0.
After the push

Where
is the mass of the astronaut,
is the mass of the satellite,
is the speed of the satellite. We can calculate the speed
of the astronaut:

So the astronaut has a opposite direction with the satellite motion, which is further away from the shuttle. Since it takes 7.5 s for the astronaut to make contact with the shuttle, the distance would be
d = vt = 1.83 * 7.5 = 13.7 m
Answer:

Explanation:
given,
velocity of particle 1 = 0.741 c to left
velocity of second particle = 0.543 c to right
relative velocity between the particle = ?
for the relative velocity calculation we have formula

u_x = 0.543 c
v_x = - 0.741 c




Relative velocity of the particle is 
Answer:
The momentum would be doubled
Explanation:
The magnitude of the momentum of the freight train is given by:

where
m is the mass of the train
v is its speed
In this problem, we have that the speed of the train is unchanged, while the mass of the train is doubled:

therefore, the new momentum is

so, the momentum has also doubled.
Answer:k=28.29 kN/m
Explanation:
Given
mass 
height from which Elevator falls 
Let x be the compression in the spring
thus From conservation of Energy Potential energy will convert in to Elastic Potential Energy of spring
----------1
also maximum acceleration is 5g
thus

here 


Substitute x in equation 1





The time must be measured with respect to gravity. As it falls, it has free fall that is the force acting on it will be the gravity.With the distance in account, d = 1/2 gt²
t = √(2d/g)