To solve this problem, we can use the equations of motion. The key is to recognize that the vertical motion of the bullet is subject to the acceleration due to gravity, while the horizontal motion is not affected.
Let's calculate the time it takes for the bullet to reach the ground.
First, let's find the time it takes for the bullet to fall vertically from a height of 80m:
We can use the equation of motion:
h = ut + (1/2)gt^2,
where h = vertical displacement (80m), u = initial vertical velocity (0 m/s since the bullet is fired horizontally), g = acceleration due to gravity (10 m/s^2), t = time.
Plugging in the values, we get:
80 = 0 + (1/2) * 10 * t^2, 80 = 5t^2, 16 = t^2.
Taking the square root of both sides, we find:
t = √16 = 4 s.
So, it takes 4 seconds for the bullet to fall vertically.
Since the bullet is fired horizontally, its horizontal velocity remains constant throughout its motion. Thus, we can calculate the horizontal distance traveled by using the formula:
s = ut,
where s = horizontal distance, u = initial horizontal velocity (800 m/s), t = time (4 s).
Plugging in the values, we get:
s = 800 * 4 = 3200 m.
Therefore, the bullet will travel a horizontal distance of 3200 meters during the time it takes to reach the ground.
In summary, it takes 4 seconds for the bullet to reach the ground, and it travels a horizontal distance of 3200 meters.