Spring powered dart gun conceptual question

[freshcoast]

1. Problem statement.
A spring powered dart gun fires darts straight downward towards the Earth from the same height each time. First it fired a regular dart, then a dart with twice the mass. Which dart takes the least time to reach the ground after exiting the gun?

A) the regular dart
B) the weighted dart
C) each takes the same time
D) there is insufficient information to answer the question.

2. Related equations
conservation of energy

3. Attempt at solution
Just to make sure I got the correct answer, would both darts take the same time to reach the floor since the energy is conserved and the mass has no effect on the velocities?

 

[voko]

The mass has no effect in the free fall. What about the motion in the gun, when masses are accelerated by the spring?

 

[freshcoast]

Oh I see, if I use the equation work done by spring = force x d, convert the f into ma, solve for a, the heavier mass would have a lower acceleration since the energy from the spring is being divided by the heavier mass?

 

[voko]

Your conclusion is correct. So what's the answer to the original question?

 

[freshcoast]

So the regular dart will take less time to reach the ground

 

[voko]

Good!