Your gun is perfectly level with a monkey at a distance of 55 m. Your bullet is shot perfectly horizontal at a speed of v_0=38 m⁄s at the exact moment the monkey lets go of the branch. How far does the monkey fall before the bullet hits it?

To determine how far the monkey falls before the bullet hits it, we need to find the time it takes for the bullet to reach the monkey and then calculate the distance the monkey falls during that time.

We know the monkey and the gun are at the same height, so the vertical motion can be ignored. The only motion we need to consider is the horizontal motion of the bullet.

The horizontal distance traveled by the bullet can be found using the equation: d = v * t, where d is the distance, v is the velocity, and t is the time.

We need to find the time it takes for the bullet to reach the monkey. Since the bullet is shot horizontally, its initial vertical velocity is 0 m/s. Therefore, we can use the equation for vertical motion to find the time it takes for the bullet to reach the monkey.

Let's consider the vertical motion of the monkey. The monkey is in free fall, so we can use the equation: d = 1/2 * g * t^2, where d is the distance, g is the acceleration due to gravity (9.8 m/s^2), and t is the time.

Since the bullet and the monkey are at the same height, the distance they both travel vertically should be equal. Therefore, we can equate the equations for the vertical motion of the monkey and the horizontal motion of the bullet to find the time:

1/2 * g * t^2 = 0

Solving for t, we get:

t = sqrt(0 / (1/2 * g)) = 0

The time, t, is 0. This means that the bullet reaches the monkey instantly, as soon as it is fired.

Therefore, the monkey doesn't have any time to fall before the bullet hits it.