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I was wondering about trajectories and ballistics.?
You have two identical rifles, both are exactly 4 feet high in rests. You fire one with the barrel level with the ground. The other rifle is angled upward 9 degrees and fired. Will both rounds travel the same distance or will one travel farther than the other?
Thanks. I thought so too, this question stemmed from a little debate about that anecdote, which the other party also did not believe even though I insisted gravity is a constant and that the longer the bullet is in the air, the farther it will go. I would like some source to show for it though.
2 Answers
- Lucas CLv 71 decade agoFavorite Answer
Hi there,
"Bored at work" (been there) is certainly correct: the angled bullet will travel further and stay in the air longer than the horizontal bullet. If you'd like some numbers to prove it, here you go:
Starting with the horizontal bullet:
The bullet has to drop 4 feet (what, no metric units?) and its initial vertical speed is zero. Let's say both rifles fire at 1000 fps. If gravity pulls the bullet downward at 32 fps², then the bullet will reach the ground after half a second (Trust me, I did the math!) During that time it will travel 500 feet horizontally. We're ignoring air resistance, by the way.
Now let's consider the angled bullet. Some of its initial 1000 fps will be vertical, and some will be horizontal. We need to apply some trig to figure out how much of the bullet's speed to allocate to each direction. I'll spare you the boring details: If the bullet is fired at 9º its horizontal speed will be about 988 fps and its vertical speed will be 156 fps.
The bullet will take about 4.9 seconds to lose its upward velocity and will reach a maximum height above ground of about 384 feet (taking into account the gun's original height). From that height it will take about the same time to return to the ground (the extra four feet on the return trip add no more than a hundredth of a second to the travel time), so we're looking at a total flight time of roughly 9.8 seconds, almost 20 times longer than the other bullet was airborne. That gives the angled bullet time to travel almost 9700 feet (1.8 miles) horizontally before hitting the ground.
As you can see, a little angle makes a big difference. If you want to give the bullet its greatest flight time and range, angle the gun at 45º.
I hope that helps you win your debate. Good luck!
- 1 decade ago
one will surely travel farther, the angled up one. more time in the air, more time to use the energy it recieved from the exlosion and gasses in the barrel. fun fact: if you shoot the level one and drop a bullet from the same hight that the rifle is shooting at, the bullet shot and the bullet dropped will both hit the ground at the same time! gravity aint she a biatch
