A rifle with a muzzle velocity of 480 m/s shoots a bullet at a target 45.6 m away. How high above the target must the rifle barrel be pointed to ensure that the bullet will hit the target? Neglect air resistance.
assuming the target is horizontal from the gun.
distance bullet falls:
h=1/2 g t^2 where the time is from
t=45.6/480 seconds
so aim h above the target.
To determine the height above the target where the rifle barrel must be pointed, we need to consider the motion of the bullet. Since the bullet is fired horizontally, the time it takes to reach the target is the same as the time it takes to fall vertically from the height at which the rifle barrel is pointed.
First, let's find the time it takes for the bullet to reach the target. We can use the formula for horizontal distance:
d = v * t
Where:
d = distance (45.6 m)
v = velocity (480 m/s)
t = time
Rearranging the formula to solve for time (t):
t = d / v
t = 45.6 m / 480 m/s
t ≈ 0.095 s
Now, since the bullet is in freefall vertically while it travels horizontally, we can use the equation:
h = (1/2) * g * t^2
Where:
h = height
g = acceleration due to gravity (9.8 m/s^2)
t = time (0.095 s)
Substituting the values:
h = (1/2) * 9.8 m/s^2 * (0.095 s)^2
h ≈ 0.045 m
So, the rifle barrel must be pointed approximately 0.045 meters (or 4.5 cm) above the target to ensure that the bullet will hit the target.