Answer: k= 
Explanation:
Recall that the formula for kinetic energy is given below as
k = 
where k=kinetic energy (joules), m= mass of object (kg), v= velocity of object m/s)
For cart A
= mass of cart A
= v = velocity of cart A
= kinetic energy of cart A
hence,
= 
For cart B
= mass of cart B
= 2v = velocity of cart B
= kinetic energy of cart B
hence,
=
= 2
from the question, both cart are identical which implies they have the same mass i.e
=
= m which implies that
and 
The total kinetic energy K is the sum of cart A and cart B kinetic energy


hence

Answer:
Height = 53.361 m
Explanation:
There are two balloons being thrown down, one with initial speed (u1) = 0 and the other with initial speed (u2) = 43.12
From the given information we make the following summary
= 0m/s
= t
= 43.12m/s
= (t-2.2)s
The distance by the first balloon is

where
a = 9.8m/s2
Inputting the values

The distance traveled by the second balloon

Inputting the values

simplifying

Substituting D of the first balloon into the D of the second balloon and solving

Now we know the value of t. We input this into the equation of the first balloon the to get height of the apartment

Answer:
Radius of the solenoid is 0.93 meters.
Explanation:
It is given that,
The magnetic field strength within the solenoid is given by the equation,
, t is time in seconds

The induced electric field outside the solenoid is 1.1 V/m at a distance of 2.0 m from the axis of the solenoid, x = 2 m
The electric field due to changing magnetic field is given by :

x is the distance from the axis of the solenoid
, r is the radius of the solenoid


r = 0.93 meters
So, the radius of the solenoid is 0.93 meters. Hence, this is the required solution.
Answer:
The final velocity of the bullet is 9 m/s.
Explanation:
We have,
Mass of a bullet is, m = 0.05 kg
Mass of wooden block is, M = 5 kg
Initial speed of bullet, v = 909 m/s
The bullet embeds itself in the block which flies off its stand. Let V is the final velocity of the bullet. The this case, momentum of the system remains conserved. So,

So, the final velocity of the bullet is 9 m/s.
Answer:

Explanation:
The fusion reaction in this problem is

The total energy released in the fusion reaction is given by

where
is the speed of light
is the mass defect, which is the mass difference between the mass of the reactants and the mass of the products
For this fusion reaction we have:
is the mass of one nucleus of hydrogen
is the mass of one nucleus of helium
So the mass defect is:

The conversion factor between atomic mass units and kilograms is

So the mass defect is

And so, the energy released is:
