Question

a bullet is fired from a gun parallel to the ground. at the exact moment it leaves the barrel, a similar bullet is dropped from the same height. which hits the ground first?
neither, they hit at same time
the one from the gun because its moving faster
the dropped one, because its not going as far
youll never find the fired one so it doesnt matter

Explanation:

Step1: Analyze vertical motion

The vertical motion of an object is governed by the equation \(h = v_{0y}t+\frac{1}{2}gt^{2}\). For the bullet fired horizontally, \(v_{0y} = 0\) (initial vertical velocity). For the dropped bullet, \(v_{0y}=0\) as well. The height \(h\) from which they start is the same.

Step2: Solve for time of fall

From \(h=\frac{1}{2}gt^{2}\), we can solve for \(t=\sqrt{\frac{2h}{g}}\). Since \(h\) (height) and \(g\) (acceleration due to gravity) are the same for both bullets, the time \(t\) it takes for them to hit the ground is the same. The horizontal motion of the fired bullet (\(x = v_{0x}t\)) does not affect its vertical fall time.

Answer:

Neither, they hit at same time.