a rifle aimed horizontally and 5 feet above level ground fires a bullet with a muzzle velocity of 3000 ft/sec. How far does the bullet travel from the end of the muzzle before it strikes the ground? (Ignore air resistance)
To find the distance the bullet travels before it strikes the ground, we can use basic principles of projectile motion. The key things to consider are the initial velocity, the acceleration due to gravity, and the angle at which the rifle is aimed.
In this case, the rifle is aimed horizontally, which means the angle of projection is 0 degrees. When the angle of projection is 0 degrees, the vertical component of velocity is 0. Hence, the bullet travels only in the horizontal direction.
Given:
Initial vertical position (y₀) = 5 feet
Vertical component of velocity (v₀y) = 0 ft/sec (since the rifle is aimed horizontally)
Horizontal component of velocity (v₀x) = 3000 ft/sec
Acceleration due to gravity (g) = 32.2 ft/sec² (assuming acceleration due to gravity on Earth)
Now, we can use the following formula to compute the horizontal distance (x) the bullet travels before it strikes the ground:
x = (v₀x * t)
where t is the time it takes for the bullet to reach the ground.
To find t, we can use the formula for time of flight in projectile motion when the bullet starts and lands at the same vertical level:
t = (2 * v₀y) / g
Since v₀y = 0, the time (t) will be 0 as well. Therefore, the bullet strikes the ground instantaneously.
So, the horizontal distance traveled by the bullet before striking the ground is 0 feet.