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 0.013 kg, and its velocity is +725 m/s. Her mass (including the gun) is 56 kg.
To solve this problem, we can use the principle of conservation of momentum.
1. Calculate the momentum of the bullet:
momentum = mass * velocity
momentum = 0.013 kg * 725 m/s
momentum ≈ 9.425 kg·m/s
2. Initially, the lead female character and the gun are at rest, so their momentum is zero.
3. Using the conservation of momentum, we can set up the equation:
Total initial momentum = Total final momentum
0 kg·m/s + 0 kg·m/s = (mass of lead female character + mass of gun) * final velocity
Since the final velocity is unknown, we need to solve for it.
4. Rearranging the equation:
(mass of lead female character + mass of gun) * final velocity = 0 kg·m/s - 9.425 kg·m/s
(mass of lead female character + mass of gun) * final velocity = -9.425 kg·m/s
5. Substituting the given values:
(56 kg + mass of gun) * final velocity = -9.425 kg·m/s
6. To find the final velocity, we need to know the mass of the gun. If it is not given, we cannot calculate the final velocity accurately.
Please provide the mass of the gun to proceed with the calculation accurately.
To solve this problem, we need to apply the principle of conservation of momentum. According to this principle, the total momentum before and after an event remains constant, provided there are no external forces acting on the system.
Let's break down the problem into a few steps.
Step 1: Find the initial momentum.
The initial momentum is the sum of the momentum of the bullet and the momentum of the woman with the gun.
Momentum of the bullet = mass of the bullet × velocity of the bullet
= 0.013 kg × 725 m/s
Momentum of the woman with the gun = mass of the woman × velocity of the woman
= 56 kg × 0 m/s (since she is standing still)
The initial momentum is the sum of the above two momenta.
Step 2: Find the final momentum.
After firing the gun, the bullet gains forward momentum, and the woman with the gun experiences backward momentum. The bullet's momentum and the woman's momentum have opposite signs.
Momentum of the bullet = mass of the bullet × final velocity of the bullet
= 0.013 kg × 725 m/s
Momentum of the woman with the gun = mass of the woman × final velocity of the woman
The final momentum is the sum of the above two momenta.
Step 3: Apply the principle of conservation of momentum.
According to the principle of conservation of momentum, the initial momentum and the final momentum should be equal.
Initial momentum = Final momentum
(0.013 kg × 725 m/s) + (56 kg × 0 m/s) = (0.013 kg × final velocity of the bullet) + (56 kg × final velocity of the woman)
Now we can solve this equation to find the final velocities of the bullet and the woman. Given that the bullet is fired forward (+) and the woman moves backward (-), we can assume the final velocity of the bullet is positive and the final velocity of the woman is negative.
Step 4: Solve for the final velocities.
(0.013 kg × 725 m/s) = (0.013 kg × final velocity of the bullet) + (56 kg × final velocity of the woman)
Plug in the known values:
0.013 kg × 725 m/s = (0.013 kg × final velocity of the bullet) + (56 kg × final velocity of the woman)
Now solve for the final velocities of the bullet and the woman.