Question

Ok, I’m going to try this question again, with the hope it makes a little more sense this time around. The details are below, but basically I'm wondering if it's possible using F=ma and gravitational force calculations to figure out the weight of a dart?

Let’s say I throw an 18 gram dart from a height of 70” and hit a target that is 77” away & 68” high. Is it possible to determine how much heavier a dart would need to be(i.e. to increase its force) to reach a target that is 3” further away, and if so, what would that weight be? The arm tempo would remain the same and I'm assuming air resistance is not a significant enough variable to consider.

Answer 1

The dart would need to weigh about `17.9 g` or very slightly less than the original dart to effect the same impact on the target moved `3` inches further away.

Explanation:

As you stated, `F = ma`.

But the only relative force on the dart in this case is the "arm tempo" which remains the same.

So here `F` is a constant, meaning that if the `a` acceleration of the dart needs to increase, the `m` mass of the dart will need to decrease.

For a difference of `3` inches over `77` inches the required change in acceleration will be minimal positive for the dart to make the same impact so the change in the weight of the dart will be slightly less.