Which hits the ground first?
06-12-2009, 03:02 PM
#16
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Very well, but I wonder; if a pitcher pitches a a fastball at 98mph parallel and at the same time - someone drops a ball at the same height; I'm inclined to believe the dropped ball will hit the ground first.
06-12-2009, 03:08 PM
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increased weight means a higher terminal velocity
06-12-2009, 03:19 PM
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also, terminal velocity is a function of the object meeting its maximum speed due to the medium it is traveling through (water, air, sand...)
you will not reach terminal velocity from a 5ft drop, but it will be something that is encountered at much greater distances.
06-12-2009, 03:20 PM
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According to the problem, the ground is perfectly flat. That gets rid of curvature of the earth idea. The acceleration due to gravity is 9.8 m/s^2 regardless of how fast something is moving. Discounting wind, friction, or any other parameter not specifically stated in the problem, they will, according to the law of gravity, hit the ground simulaneously.
"centerline of the bore" means that the exact middle of the projectile will be 36" off the ground.
The weight of the round, fired or unfired, shouldn't make a difference either, as there is not enough distance (only 3 feet) to reach terminal velocity anyway.
Besides, without a constant of friction for the fired and unfired projectiles against the air itself, there is not enough from which to draw a conclusion as to which will fall faster.
The answer is, the same time without more data.
"centerline of the bore" means that the exact middle of the projectile will be 36" off the ground.
The weight of the round, fired or unfired, shouldn't make a difference either, as there is not enough distance (only 3 feet) to reach terminal velocity anyway.
Besides, without a constant of friction for the fired and unfired projectiles against the air itself, there is not enough from which to draw a conclusion as to which will fall faster.
The answer is, the same time without more data.
06-12-2009, 03:22 PM
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If the fired bullet travels only a short distance, then yes, both bullets hit the ground at the same time.
However, if the fired bullet travels far enough, the earth, being round, CURVES AWAY FROM IT. (Remember Newton's first law of motion: moving objects tend to travel in a straight line.)
Since the fired bullet has farther to fall, it takes longer to hit the earth, so the dropped bullet hits the ground first (by a teeny-tiny fraction of a second).
However, if the fired bullet travels far enough, the earth, being round, CURVES AWAY FROM IT. (Remember Newton's first law of motion: moving objects tend to travel in a straight line.)
Since the fired bullet has farther to fall, it takes longer to hit the earth, so the dropped bullet hits the ground first (by a teeny-tiny fraction of a second).
so i would say that the shot bullet will hit first due to gravitational pull towards earth. it may be shot at a parallel angle to the ground, but as soon as it leaves the barrel of the gun gravity is pushing down on it
06-12-2009, 03:23 PM
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weight does not affect the acceleration of an object due to the pull of gravity.
also, terminal velocity is a function of the object meeting its maximum speed due to the medium it is traveling through (water, air, sand...)
you will not reach terminal velocity from a 5ft drop, but it will be something that is encountered at much greater distances.
also, terminal velocity is a function of the object meeting its maximum speed due to the medium it is traveling through (water, air, sand...)
you will not reach terminal velocity from a 5ft drop, but it will be something that is encountered at much greater distances.
I haven't taken a physics class since sophomore year of high school
06-12-2009, 03:32 PM
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They hit at the same point in time. Gravity acts equally on both bullets, regardless of horizontal speed (ie being fired or not). Mass plays no role in their speed to the ground.
Converting 36" to meters, I find that the dropped bullet reaches a final velocity of 4.223 m/s the instant before touching the ground. As such, it takes 0.431 seconds to hit. Since the same gravitation force applies to the fired bullet, we now know that it will be airborne for the same amount of time, so at 3400 f/s, the bullet travels 1465 feet away from the gun before touching down (constant horizontal velocity strictly assumes no air drag).
Now, as to the question of the curvature of the earth. While valid at higher velocities (like orbital or sub orbital velocities in the 20,000 mph range), it is not the case here. The circumference of the earth is something like 131 million feet (if my units are right), which means the angle subtended by the traveling bullet along the surface arc of the earth (in 0.431s) is a measly 0.000012 degrees. This is also known as 'jack sh$t'. By use of the small angle approximation, the curvature of the earth plays no meaningful role in this problem.
Converting 36" to meters, I find that the dropped bullet reaches a final velocity of 4.223 m/s the instant before touching the ground. As such, it takes 0.431 seconds to hit. Since the same gravitation force applies to the fired bullet, we now know that it will be airborne for the same amount of time, so at 3400 f/s, the bullet travels 1465 feet away from the gun before touching down (constant horizontal velocity strictly assumes no air drag).
Now, as to the question of the curvature of the earth. While valid at higher velocities (like orbital or sub orbital velocities in the 20,000 mph range), it is not the case here. The circumference of the earth is something like 131 million feet (if my units are right), which means the angle subtended by the traveling bullet along the surface arc of the earth (in 0.431s) is a measly 0.000012 degrees. This is also known as 'jack sh$t'. By use of the small angle approximation, the curvature of the earth plays no meaningful role in this problem.
Last edited by shagginwagon; 06-12-2009 at 03:35 PM.
06-12-2009, 03:48 PM
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if you think that this situation is bizarre (which you shouldn't, because it's basic mechanical physics) then you will be even more surprised to experiment with different weights on a pendulum of fixed length
06-12-2009, 03:51 PM
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Interesting discussion, however, I have a question..... if this quote is true, then I would expect this to hold true for a bullet as well. That said....if the barrel was rifled, then the bullet would effectively be spinning when it left the muzzle of the gun. Wouldn't that be essentially the same as putting spin on a baseball?
