Bullet Drop vs. Bullet Shot: Which Reaches the Ground First?

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When a bullet is dropped from a height of 5 feet and another is shot horizontally from the same height, both will reach the ground simultaneously, assuming negligible air resistance. This phenomenon occurs because horizontal and vertical motions are independent of each other. Additionally, if a bullet is fired from ground level aimed at a bullet dropped from above, the two bullets will collide regardless of the speed of the fired bullet. This illustrates fundamental principles of physics regarding projectile motion and gravity. The discussion emphasizes the importance of scientific understanding over common misconceptions.
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My question is not homework, but a simple physics question that caused discussion (and differing opinions from people with no scientific background) and needs a scientific answer:

If one person dropped a bullet from 5 feet and another person shot a bullet at a height of 5 feet, would they both reach the ground at the same time?
 
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Yes, if the bullet is shot horizontally.
 
jklamont said:
My question is not homework, but a simple physics question that caused discussion (and differing opinions from people with no scientific background) and needs a scientific answer:

If one person dropped a bullet from 5 feet and another person shot a bullet at a height of 5 feet, would they both reach the ground at the same time?
What is even more intriguing is that if one person dropped a bullet B1 from any height and another bullet B2 was fired from a gun at ground level aimed at B1 at the exact moment B1 was dropped, the two bullets would collide no matter how fast B2 was fired.
 
That is all assuming, of course, that air resistance is negligible. It is based on the fact that horizontal and vertical motion are independent.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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