bull's-eye bob at a hunting range fires his rifle at a target 200 meters downrange. the bullet moves horizontally from the rifle barrel with a speed of 400 m/s? how far does the bullet drop from a straight line horizontal path bny the time it reaches the target
To find out how far the bullet drops from a straight-line horizontal path by the time it reaches the target, we need to calculate the vertical displacement (drop) of the bullet.
First, let's determine how long it takes for the bullet to reach the target. We can use the formula:
time = distance / speed
Given:
Distance = 200 meters
Speed = 400 m/s
time = 200 / 400
time = 0.5 seconds
Since the bullet moves horizontally, there is no acceleration in the horizontal direction. Therefore, the vertical displacement (drop) can be calculated using the formula:
displacement = 0.5 * acceleration * time^2
The acceleration due to gravity is approximately 9.8 m/s².
displacement = 0.5 * (-9.8) * (0.5^2)
displacement = -1.225 meters
Hence, the bullet drops approximately 1.225 meters from a straight-line horizontal path by the time it reaches the target.
To find out how far the bullet drops from a straight-line horizontal path, we can use the principles of projectile motion.
First, let's assume that air resistance is negligible.
In projectile motion, the horizontal and vertical motions are independent. So, we can separately calculate the horizontal distance traveled by the bullet and the vertical distance it drops.
Given:
Initial horizontal speed (Vx) = 400 m/s
Vertical acceleration due to gravity (ay) = 9.8 m/s²
Time of flight (t)
We need to find the time of flight (t) of the bullet, which is the time it takes for the bullet to reach the target.
We can use the equation:
Range (R) = horizontal speed (Vx) x time of flight (t)
Since the range is 200 meters, we can rearrange the equation to solve for the time of flight:
t = R / Vx
Substituting the given values:
t = 200 m / 400 m/s
t = 0.5 seconds
Now that we have the time of flight, we can calculate the vertical distance dropped by the bullet.
Using the equation of motion:
Vertical distance (d) = 0.5 x acceleration (ay) x time (t)²
Substituting the given values:
d = 0.5 x 9.8 m/s² x (0.5 s)²
d = 0.5 x 9.8 m/s² x 0.25 s²
d = 1.225 meters
Therefore, the bullet drops approximately 1.225 meters from a straight-line horizontal path by the time it reaches the target.
Note: This calculation assumes a flat and level range, neglects the effects of air resistance, and assumes the bullet is fired at an angle close to the horizontal.
Dx = Xo*Tf = 200 m.
400 * Tf = 200
Tf = 0.5 s. = Fall time.
d = 0.5g*Tf^2 = 4.9*0.5^2 = 1.23 m.