OK, assume that an object with mass M is thrown with X amount of force. This object would travel a distance, D.
How would increasing M, while leaving X unchanged cause an increase in D?
For example, if I throw a nerf dart as hard as I can, it will only travel so far. However, if I add weight to the nerf dart, I can throw it much farther. Why does this work?
Also, why would the same not apply for the dart being shot from the nerf gun, or would it?
I believe it has something to do with air-resistance and trajectory, are there any formulas I can use to prove this?
Not homework, just a discussion with a friend. I don't have physics until next semester.
Best Answer
Your problem is that you are assuming a constant force. This is difficult to deliver. Since $F=ma$, in order to maintain a constant force as the mass decreases, the acceleration has to increase. For small masses, your arm can't accelerate fast enough to generate the required force.
It's easy to push on a baseball with 10N of force. It's very difficult to push on a pea with 10N. You may be pushing hard to throw the nerf dart, but most of that effort is going into accelerating your arm. By adding mass, your limited acceleration is able to apply a larger force to the dart.