The lead female character in the movie Diamonds Are Forever is standing at the edge of an offshore oil rig. As she fires the gun, she is driven back over the edge and into the sea. Suppose the mass of a bullet is 0.009 kg, and its velocity is +712 m/s. Her mass (including the gun) is 50 kg.
(a) What recoil velocity does she acquire in response to a single shot from a stationary position, assuming that no external force keeps her in place?
m/s
(b) Under the same assumption, what would be her recoil velocity if, instead, she shoots a blank cartridge that ejects a mass of 5.0 10-4 kg at a velocity of +712 m/s?
m/s
Use momentum conservation. Please show your work if further assistance is needed.
a) (.009*712)/50=.12816 m/s, this answer is not right. what am I doing wrong.
Recoil will be in the negative direction.
To determine the recoil velocity of the lead female character in the movie Diamonds Are Forever, we can use the principle of conservation of momentum. According to this principle, the total momentum before and after the event remains constant, assuming no external forces act on the system.
Let's calculate the recoil velocity in each case:
(a) When she fires a bullet:
The initial momentum is zero since she is standing at a stationary position.
The final momentum is the sum of the bullet's momentum and her momentum after firing the gun.
We can use the equation: initial momentum = final momentum.
Initial momentum = 0
Final momentum = (bullet mass) × (bullet velocity) + (her mass) × (recoil velocity)
Since the bullet is fired, its velocity is positive, while the recoil velocity of the character will be negative as she is driven back.
So, the equation becomes: 0 = (0.009 kg) × (712 m/s) + (50 kg) × (recoil velocity)
Simplifying the equation, we get: (0.009 kg) × (712 m/s) = -(50 kg) × (recoil velocity)
Now, we can solve for the recoil velocity:
recoil velocity = (0.009 kg × 712 m/s) / -50 kg
Calculating the value, we find: recoil velocity ≈ -0.128 m/s
Therefore, the recoil velocity she acquires when firing a single bullet is approximately -0.128 m/s.
(b) When she fires a blank cartridge:
Using the same principle, the initial momentum is still zero.
The final momentum is the sum of the ejected mass's momentum and her momentum.
Again, we use the equation: initial momentum = final momentum.
Initial momentum = 0
Final momentum = (ejected mass) × (ejected velocity) + (her mass) × (recoil velocity)
Since the ejected mass is moving forward with a positive velocity, her recoil velocity will be negative once again.
So, the equation becomes: 0 = (5.0 × 10^-4 kg) × (712 m/s) + (50 kg) × (recoil velocity)
Simplifying the equation, we get: (5.0 × 10^-4 kg) × (712 m/s) = -(50 kg) × (recoil velocity)
Solving for the recoil velocity:
recoil velocity = (5.0 × 10^-4 kg × 712 m/s) / -50 kg
Calculating the value, we find: recoil velocity ≈ -0.00712 m/s
Therefore, her recoil velocity when shooting a blank cartridge is approximately -0.00712 m/s.