# Relative Velocity Changes

• Strasz
In summary, when an object in motion suddenly, dramatically increases in mass, its velocity decreases by a factor m'/m.f

#### Strasz

While playing a rousing game of Dungeons and Dragons, we came upon a strange question that I thought might best be answered by the fine people at these forums.

A tree polymorphed into an arrow, when fired from the bow will transform back into a sharpened log. What then happens to the speed of the projectile? Will it continue flying at that speed? Or will it slow down? Will it simply fall to the ground?

Basically, what happens when an object in motion suddenly, dramatically increases in mass? Assume standard gravity and air resistance.

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Objects don't suddenly increase in mass, but if they did, momentum would still have to be conserved. Let primed quantities (with a prime symbol ' after them) represent the quantities after the "mass increase." Momentum is mass x velocity, so

mv = m'v'

v' = m/m' v

The velocity would decrease by a factor m'/m.

Edit: you asked about gravity too. Since the horizontal velocity is reduced, but the vertical accleration remains the same, the vertical velocity increases at the same rate as before the mass increase, and so the time taken to reach the ground is the same. Therefore, the object will not travel as far horizontally before reaching the ground as it would have if the mass increase hadn't occured. Another way to think about it: the shape of the parabolic trajectory of the object would change.

Thanks a bunch!

It depends on what "polymorphing" is. Does it violate or conserve momentum...

If we are breaking the laws of nature anyway, we might as well break the conservation of momentum.

Look at it from the arrows perspective, i.e. you are an observer sitting on the arrow. Why should the world around the arrow suddenly slow down just because the mass of the arrow increases? That seems even worse to me than violation of conservation of momentum.