A cannon is mounted on a railway flatcar, the muzzle elevated to 31.4° and pointed in the direction of the track. The cannon fires a 1.10-metric-ton projectile at 1.10 km/s.
(a) If the flatcar and cannon together have a mass of 36.0 metric tons (not including the projectile), what is the initial recoil speed of the flatcar?
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To find the initial recoil speed of the flatcar, we can use the principle of conservation of momentum. According to this principle, the total momentum before firing should be equal to the total momentum after firing.
Let's break down the problem step by step:
Step 1: Calculate the momentum of the cannonball.
The momentum of an object can be calculated using the formula:
momentum = mass * velocity
In this case, the mass of the projectile is given as 1.10 metric tons (which is 1100 kg), and the velocity is given as 1.10 km/s.
momentum of the projectile = 1100 kg * 1.10 km/s
Step 2: Calculate the momentum of the cannon and the flatcar.
The mass of the cannon and flatcar together is given as 36.0 metric tons (which is 36,000 kg). But we need to convert it into momentum by multiplying it with the recoil speed of the flatcar.
momentum of the cannon and flatcar = 36,000 kg * recoil speed of the flatcar
Step 3: Apply the conservation of momentum principle.
According to the principle of conservation of momentum, the total momentum before firing is equal to the total momentum after firing.
momentum of the cannonball = momentum of the cannon and flatcar
1100 kg * 1.10 km/s = 36,000 kg * recoil speed of the flatcar
Step 4: Solve for the recoil speed of the flatcar.
To find the recoil speed of the flatcar, we rearrange the equation:
recoil speed of the flatcar = (1100 kg * 1.10 km/s) / 36,000 kg
Now, you can calculate the recoil speed of the flatcar by plugging in the values:
recoil speed of the flatcar = (1100 kg * 1.10 km/s) / 36,000 kg
After performing the calculation, you will get the final answer for the initial recoil speed of the flatcar.