## Monday, October 31, 2011

### "Feet" is not the same as "Feet per Second"

One guy was talking about a pellet gun that shoots pellets at 1200 feet per second.

The other guy said, "1200 feet! That's two football fields. That's pretty far."

I said nothing, because I don't know. But the pellets don't go 1200 feet.

If gravity pulls the pellet down at 16 feet per second, and if you are holding the gun about four feet above level ground (and shooting level) then the pellet will be in the air only about a quarter of a second. So it will travel about 300 feet.

Jazzbumpa said...

"Feet per second" is not the same as "feet per second squared."

Recalculating . . .

Cheers!
JzB

Clonal said...

G = (32 f per s) per s

Clonal said...

But of course, the average vertical velocity over that 1 sec is 16 ft/sec. But for maximum range, the gun has to be fired at an angle of ~45 deg depending upon the height of the gun above the ground

Jazzbumpa said...

By my crude calculation, it will travel 588 ft.

Cheers!
JzB

Jazzbumpa said...

That's from a ht. of 4 ft. fired in an exactly horizontal trajectory.

Cheers!
JzB

Clonal said...

Jazz

A drop of 4 ft takes a 1/2 sec, so, in the absence of air resistance, the pellet should travel a horizontal distance of 600 feet.

Jazzbumpa said...

Clonal -

This is a calculus problem and I haven't done calculus in over 40 years. (Never was any good at it, but that's another story.)

I used a tabular method, taking the acceleration to be .16 ft/Sec^2 for each .01 sec. Estimated travel in first .01 sec to be .08 ft. Each additional .01 sec, velocity increases by .16 ft/sec.

In 0.49 sec, velocity is 15.69 f/sec, vertical distance traveled is 3.9968ft.

0.49*1200 = 588 ft.

We differ by .01 sec.

Cheers!
JzB

The Arthurian said...

588? That's just a rounding error, Jazz. I think you guys are right.

Try this:

Gravity creates a constant acceleration. On a graph, "constant" is a straight line. On a graph of velocity (y-axis) and time (x-axis), velocity starts at zero, and ends one second later at 32 feet per second. The straight, upsloping line represents acceleration.

At 0 seconds, velocity is zero. At ½ second, velocity has reached 16 FPS, and the average velocity is 8 FPS.

Travel 8 FPS for 0.5 seconds, and you have moved 4 feet (downward), at which time the pellet hits the ground. And in that 0.5 seconds, the pellet travels 600 ft horizontally.

Of course, if the guy is shooting rodents, he's probably aiming downhill, and then the horizontal travel will be less...