can someone explain how to do this step by step i already have the answer but i need to know how to do it!!
the answer is (a)6.67m/s (b)111km/s^2
The muzzle velocity of 50g shell leaving a 3kg rifle 400m/s(a)What is the recoil velocity of the rifle?(b)If the bullet travel 72cm before leaving the end of the barrel, at what rate what the bullet accelerated?
To find the recoil velocity of the rifle, we can use the principle of conservation of momentum. The momentum before firing is equal to the momentum after firing.
Step-by-step explanation:
Step 1: Determine the initial momentum.
- Given mass of the shell (m1): 50g = 0.05kg
- Given muzzle velocity of the shell (v1): 400m/s
- Calculate the initial momentum (p1): p1 = m1 * v1
Step 2: Determine the final momentum.
- Given mass of the rifle (m2): 3kg
- Let the recoil velocity of the rifle be v2 (what we are trying to find)
- Calculate the final momentum (p2) using the formula: p2 = m2 * v2
Step 3: Apply the conservation of momentum.
- According to the conservation of momentum, p1 = p2.
- Equate the initial and final momentum: m1 * v1 = m2 * v2
- Substitute the given values: 0.05 * 400 = 3 * v2
- Solve for v2: v2 = (0.05 * 400) / 3
- Calculate the recoil velocity of the rifle: v2 = 6.67m/s (a)
For the second part of the question:
To find the acceleration of the bullet, we can use the kinematic equation relating displacement, initial velocity, final velocity, acceleration, and time.
Step-by-step explanation:
Step 1: Determine the initial velocity.
- Given muzzle velocity of the shell (v1): 400m/s
Step 2: Determine the final velocity.
- Let the final velocity be v2 (which is the velocity when the bullet leaves the end of the barrel).
- Given displacement (s): 72cm = 0.72m
- Use the equation: v2^2 = v1^2 + 2as
- Substitute the given values: v2^2 = 400^2 + 2 * a * 0.72
Step 3: Determine the acceleration.
- Rearrange the equation to solve for acceleration: a = (v2^2 - v1^2) / (2 * s)
- Substitute the given values: a = (v2^2 - 400^2) / (2 * 0.72)
- Calculate the acceleration of the bullet: a = 111km/s^2 (b)
So, the recoil velocity of the rifle is 6.67m/s (a), and the acceleration of the bullet is 111km/s^2 (b).