# Thread: pellet gun physics problem

1. ## pellet gun physics problem

any help with this is greatly appreciated please.

A pellet gun is fired straight downward from the edge of a cliff that is 16 m above the ground. The pellet strikes the ground with a speed of 26 m/s. How far above the cliff edge would the pellet have gone had the gun been fired straight upward?
how many meters?

2. It's a standard setup. You must know only these:

a(t) = -g -- g is acceleration due to gravity

v(t) = -g*t + v0 -- v0 is the initial velocity that we are not given.

s(t) = -½g*t^2 + v0*t + h0 -- h- is the initial height that we are given.

So,

s(t) = -½g*t^2 + v0*t + 16 m

It hits the ground when? s(t) = 0

0 = -½g*t^2 + v0*t + 16 m

This gives the slightly untidy $t_{impact} = \frac{1}{g}\left(v_{0}+\sqrt{v_{0}^{2}+32*g* m}\right)$.

There's another solution, but it's negative and I'm sure we don't want that.

We are given the velocity on impact.

$v(t_{impact}) = 26 m/s$

That should lead you to the initial velocity. (Hint: I get a little over 19 m/s)

Once you have that, you are on your way to a simple solution of the maximum of a parabola.

Specifically there is a coordinate system defined here that has an origin at the bottom of the cliff, and the positive s direction is defined to be upward.

(I feel it is crucial to make a mention of these things. )

-Dan

4. Kinetic energy generates a velocity with which the projectile leaves the barrel while the ballistic coefficient and sectional density determine the damage to the target.
Therefore, guns don’t kill people, physics does.

5. Originally Posted by galactus
Kinetic energy generates a velocity with which the projectile leaves the barrel while the ballistic coefficient and sectional density determine the damage to the target.
Therefore, guns don’t kill people, physics does.
What on Earth are you talking about??

If someone is hit in the toe with a bullet they don't die. If they get hit in the heart, they are very likely to die.

Thus guns don't kill people nor does physics: physiology kills people.

-Dan

6. For heaven's sake, it's a joke. It is a quote from John Lithgow's character on "3rd Rock from the Sun".

7. Originally Posted by galactus
For heaven's sake, it's a joke. It is a quote from John Lithgow's character on "3rd Rock from the Sun".
Ummm... My reparte was a joke as well...

-Dan

8. Originally Posted by topsquark
(I feel it is crucial to make a mention of these things. )
Right. As soon as I walked away, I somewhat regretted two things:

1) Lack of more clear definitions.
2) The sign of 'g'.

Anyway, if you can sort it out, it was worth it.