The rest energy of a particle is

where

is the rest mass of the particle and c is the speed of light.
The total energy of a relativistic particle is

where v is the speed of the particle.
We want the total energy of the particle to be twice its rest energy, so that

which means:


From which we find the ratio between the speed of the particle v and the speed of light c:

So, the particle should travel at 0.87c in order to have its total energy equal to twice its rest energy.
The velocity of Satellite A is 2% greater than velocity of satellite B.
The given parameters;
- <em>Altitude of Satellite A = 500 km</em>
- <em>Altitude of Satellite B = 800 km</em>
The forces acting on the Satellites are given as follows;


Thus, the velocity of Satellite A is 2% greater than velocity of satellite B.
Learn more about velocity of satellite here: brainly.com/question/13981089
Answer:
√2
Explanation:
If the final kinetic energy is 2 times the initial kinetic energy:
KE = 2 KE₀
½ mv² = 2 (½ mv₀²)
v² = 2 v₀²
v = √2 v₀
Therefore, the ratio of the final momentum to the initial momentum is:
p / p₀
mv / (mv₀)
v / v₀
√2
Answer:

Explanation:
Total =40 miles.
y miles at x miles/hr.
40- y miles at 1.25 x miles/hr.\
We know that
Distance = time x velocity
For y miles
Lets time taken to cover y miles is t
y = x t
t=y/x -----------1
For 40- y
Lets time taken to cover 40- y is t'
40- y = 1.25 x t'
t'=(40-y)/1.25x -----------2
By adding both equation
t+t'=y/x + (40-y)/1.25x
t+t'=(32+0.2y)/x
Now lets time T taken by Marla if she will travel at x miles per hr for entire trip.
40 = x T
T=40/x
So

To find numerical value of above expression we have to know the value of y.
Answer:
the equation of motion is

Explanation:
Given that,
The weight attached to the spring is 24pounds
Acceleration due to gravity is 32ft/s²
Assume x is the string length, 4inches
convert the length inches to to feet = 4/12 = 1/3feet
From Hookes law , we calculate the spring constant k
k = W / x
k = 24 / (1/3)
k = 24 / 0.33
k = 72lb/ft
If the mass is displace from its equilibrium position by amount x
the differential equation is


Auxiliary equation is

Thus the solution is,


The mass is release from rest
x'(0) = 0

Therefore
x(t) = c₁ cos4 √6t
x(0) = -2inches
c₁ cos4 √6(0) = 2/12feet
c₁= 1/6feet
There fore, the equation of motion is
