how long for the bullet to hit the ground? Physics

Question

A bullet is fired from a rifle that is held 1.54 m above the ground in a horizontal orientation. The initial speed of the bullet is 1117 m/s. Calculate the time it takes for the bullet to strike the ground.

Answer 1

What happens to the bullet can be broken into what happens in two independent directions, the up/down (typically noted as the y-direction) and the back/forth (typically noted as the x-direction), In this case, all of the initial 1117 m/s velocity is happening in the horizontal direction. Since there is no initial velocity in the y-direction, we can consider what happens in the y-direction to be the same as an object dropped from 1.54 m

y = v_yit + 1/2a_yt² where y = -1.54 m (it is 1.54 m down to the ground), v_yi = 0 (the initial velocity in the y-direction is zero), and a_y = -9.81 m/s²

So -1.54 = (0)t + (-9.81)t²

-1.54 = -9.81t²

1.54/9.81 = t²

t = √(1.54/9.81) = 0.396

The time it takes to hit the ground is 0.396 seconds

Note that during that time it travels quite some distance in the horizontal direction but that does NOT effect the time it takes to hit the ground.