Answer: 40.4M/s
Solution: 46.6/1.15 = 40.4347826 then round it to a single decimal point, since 3 is lower than 5 it will be rounded to 40.4
Answer:

Explanation:
We must separate the motion into two parts, the first when the rocket's engines is on and the second when the rocket's engines is off. So, we need to know the height (
) that the rocket reaches while its engine is on and we need to know the distance (
) that it travels while its engine is off.
For solving this we use the kinematic equations:
In the first part we have:

and the final speed is:

In the second part, the final speed of the first part it will be the initial speed, and the final speed is zero, since gravity slows it down the rocket.
So, we have:

The sum of these heights will give us the total height, which is known:

This is the time that its needed in order for the rocket to reach the required altitude.
Answer:
The speed of its center of mass =
Explanation:
Consider the potential energy at the level of center of mass of rod below the pivot=0
Mass of uniform rod=M
Length of rod=L
The rotational inertia about the end of a uniform rod=
Kinetic energy at the level of center of mass of rod below the pivot=
Kinetic energy at the level of center of mass of rod above the pivot=0
Potential energy at the level of center of mass of rod above the pivot=mgh
We have to find the center of mass ( in terms of g and L).
According to conservation of law of energy
Initial P.E+Initial K.E=Final P.E+Final K.E

Where 
I=Moment of inertia
=Angular velocity
Substitute the values then we get


Now, we know that
, 
Substitute the values then we get





Hence, the speed of its center of mass =
The velocity equation is 
Known facts:
- t = 3.83s
- a= -3.04
- intial velocity = 0
Plug into equation known quantities:

Thus the final velocity is -11.6432m/s
Hope that helps!
Answer:
a) 
b) 
c) 
d) 
e) 
Explanation:
At that energies, the speed of proton is in the relativistic theory field, so we need to use the relativistic kinetic energy equation.
(1)
Here β = v/c, when v is the speed of the particle and c is the speed of light in vacuum.
Let's solve (1) for β.

We can write the mass of a proton in MeV/c².

Now we can calculate the speed in each stage.
a) Cockcroft-Walton (750 keV)



b) Linac (400 MeV)



c) Booster (8 GeV)



d) Main ring or injector (150 Gev)



e) Tevatron (1 TeV)



Have a nice day!