Question

The rifles in the figures are being fired horizontally (straight outward, off platforms). The bullets fired from the rifles are all identical, but the rifles propel the bullets are different speeds. The speed of each bullet and the height of each platform are given. All the bullets miss their targets and hit the ground. Rank the time it takes the bullets to hit the ground. Explain your reasoning.

Answer 1

Answer:

  t = √ 2y₀ / g

if they are at the same height, all the bullets must carry the target, since when advancing the height decreases

Explanation:

In this exercise we see that the bullets are fired horizontally so the time it takes to reach the ground is

          y = y₀ + $v_{oy}$  t - ½ g t²

as they are fired horizontally their vertical velocity is zero and the height upon reaching the ground is zero y = 0

         0 = y₀ - ½ g t²

         t = √ 2y₀ / g

from here we can see that the time it takes for the bullets to hit the floor depends only on the initial height

Therefore, all the bullets that come out of the same height reach the ground at the same time, but at a different distance, so if one misses the target, everything must fail since reaching the target is below the initial height.

The horizontal distance traveled by the bullets is

        x = v₀ₓ t

        v₀ₓ =v₀

        x = v₀ √2y₀/g

For a more precise calculation we should know the height of the target and the bullets, but if they are at the same height, all the bullets must carry the target, since when advancing the height decreases