a bullet is fired horizontally with a velocity of 40 m/s from a height if 50m. how far it will fall to the ground
50m, of course.
you want to rephrase the question?
also, recall that the height h is
h = 50 - 4.9t^2
use that t in figuring
distance = speed * time
15.8m
To determine how far the bullet will fall to the ground, we can use the equation for vertical motion:
h = (1/2) * g * t^2
Where:
h is the height (in meters) the bullet falls
g is the acceleration due to gravity (approximately 9.8 m/s^2)
t is the time taken (in seconds) for the bullet to fall to the ground
First, we need to find the time it takes for the bullet to fall to the ground. Since the bullet is fired horizontally with a velocity of 40 m/s, its initial vertical velocity is 0 m/s. Using the equation:
h = (1/2) * g * t^2
50 = (1/2) * 9.8 * t^2
Simplifying:
50 = 4.9 * t^2
Divide both sides by 4.9:
10 = t^2
Taking the square root of both sides:
t = √10 ≈ 3.16 s
So it takes approximately 3.16 seconds for the bullet to fall to the ground.
Now we can substitute the value of t back into the original equation to find the distance fallen:
h = (1/2) * g * t^2
h = (1/2) * 9.8 * (3.16^2)
h ≈ 49.05 m
Therefore, the bullet will fall approximately 49.05 meters to the ground.
To find how far the bullet will fall to the ground, we can use the equations of motion.
First, we need to calculate the time it takes for the bullet to hit the ground. Since the bullet is fired horizontally, the initial vertical velocity is zero. The only force acting on the bullet is gravity, which accelerates the bullet downwards at 9.8 m/s². The initial height of the bullet is 50 m.
Using the equation for vertical displacement:
y = v₀t + (1/2)gt²
Where:
- y is the vertical displacement (height)
- v₀ is the initial vertical velocity (zero)
- t is the time taken
- g is the acceleration due to gravity (9.8 m/s²)
Since the bullet is falling vertically downward, the height (y) will be -50 m (negative because it is below the reference point).
-50 = 0*t + (1/2)*(-9.8)*t²
Simplifying the equation:
-50 = -4.9t²
Rearranging the equation:
t² = 50/4.9
t² ≈ 10.20
Taking the square root of both sides:
t ≈ √10.20
t ≈ 3.19 seconds (rounded to two decimal places)
Now, to find the horizontal distance traveled by the bullet during this time, we can use the equation:
x = v₀x * t
Where:
- x is the horizontal distance
- v₀x is the initial horizontal velocity (40 m/s, given in the question)
- t is the time taken (3.19 seconds, calculated above)
Plugging in the values:
x = 40 m/s * 3.19 s
x ≈ 127.6 meters
Therefore, the bullet will fall approximately 127.6 meters horizontally to the ground.