The lead female character in the movie Diamonds Are Forever is standing at the edge of an offshore oil rig. As she fires a gun, she is driven back over the edge and into the sea. Suppose the mass of a bullet is 0.012 kg, and its velocity is +715 m/s. Her mass (including the gun) is 48 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?
(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 +715 m/s?
I thought this is what i was supposed to do. But it is not giving me the right answer
a) v = (m/M)U = (.012/48)*715 = .178 mps recoil
b) v = (m/M)U = (5E-4/48)*715 = .007 mps recoil ANS
you did it correct. I hope you are not putting in mps for m/s
no that is not a problem. I just have to put in the number. the label is provided.
I figured it out. the velocity of the recoil is in the negative direction.
I HAVE NO IDEA:D
To solve this problem, we can use the principle of conservation of momentum. The total momentum before the gunshot is equal to the total momentum after the gunshot.
(a) To find the recoil velocity when she fires a bullet, we can calculate the total momentum before and after the gunshot.
Total momentum before the gunshot:
Initial momentum = 0 (since she is stationary)
Total momentum after the gunshot:
The momentum of the bullet = mass of the bullet * velocity of the bullet = 0.012 kg * 715 m/s
The recoil velocity can be calculated by dividing the momentum of the bullet by the total mass of the woman and the gun:
Recoil velocity = (momentum of the bullet) / (mass of the woman + mass of the gun)
Recoil velocity = (0.012 kg * 715 m/s) / (48 kg)
By calculating this, the recoil velocity is approximately 0.178 m/s.
(b) For the case when she fires a blank cartridge, we need to consider the momentum of the ejected mass in addition to the woman's mass and the gun.
Total momentum before the gunshot:
Initial momentum = 0 (since she is stationary)
Total momentum after the gunshot:
The momentum of the ejected mass = mass of ejected mass * velocity of ejected mass = 5.0 * 10^-4 kg * 715 m/s
The recoil velocity can be calculated by dividing the total momentum after the gunshot by the total mass of the woman, the gun, and the ejected mass:
Recoil velocity = (momentum of the ejected mass) / (mass of the woman + mass of the gun + mass of the ejected mass)
Recoil velocity = (5.0 * 10^-4 kg * 715 m/s) / (48 kg)
By calculating this, the recoil velocity is approximately 0.007 m/s.