Answer:
a)
, b)
, c) 
Explanation:
a) The change in the gravitational potential energy of the marble-Earth system is:


b) The change in the elastic potential energy of the spring is equal to the change in the gravitational potential energy, then:

c) The spring constant of the gun is:




First, we convert kcal to joules:
1 kcal = 4.184 kJ
475 kcal = 1987.4 kJ
Now, calculating the change in internal energy:
ΔU = Q + W; where Q is the heat supplied to the system and W is the work done on the system.
ΔU = -500 + 1987.4
ΔU = 1487.4 kJ
Answer:
A and C are 180 deg out of phase (opposite points on a 360 deg wave)
Supposing velocity is speed and direction, and momentum is mass*velocity, if the velocity increases by a factor of 5, then so should the momentum regardless of the whole space thing.