1) A 10 kg car is moving at 44 m/s when it collides with a stationary 71 kg truck. The two cars interlock and move off at what speed
2) A 9 kilogram potato leaves a 155 kilogram cannon with a velocity of 283 m/s. What is the recoil velocity of the launcher?
3) A 994 kg truck moves to the right at 17 m/s and collides with a 700 kg car that is moving at 5 m/s. If the two vehicles stick together, what will their velocity be after the collision?
4) Steve loosely holds a 2.4 kg air rifle and fires a 0.3 kg bullet. The velocity of the bullet is 267.9 m/s. What is the recoil velocity of the rifle?
momentum is conserved in all these problems
that is some BIG potato in #2
watermelon?
9 * 283 + 155 u = 0 which is the momentum before ignition.
1) To determine the speed at which the two cars move off after the collision, we can apply the principle of conservation of momentum. According to this principle, the total momentum before the collision should be equal to the total momentum after the collision.
The momentum of an object can be calculated by multiplying its mass by its velocity. Therefore, the momentum of the car before the collision can be calculated as:
Momentum of car = mass of car * velocity of car = (10 kg) * (44 m/s) = 440 kg·m/s
Since the truck is stationary, its initial momentum is zero.
After the collision, the two cars interlock and move off together, so they have a common final velocity, let's call it v.
The total momentum after the collision is the sum of the momentum of the car and the truck, which can be expressed as:
Total momentum after = (mass of car + mass of truck) * final velocity = (10 kg + 71 kg) * v
According to the conservation of momentum, the total momentum before and after the collision should be equal. Therefore, we can set up an equation:
440 kg·m/s = (10 kg + 71 kg) * v
Now we can solve for the final velocity (v):
v = 440 kg·m/s / (10 kg + 71 kg) = 440 kg·m/s / 81 kg ≈ 5.43 m/s
Therefore, the two cars move off at a speed of approximately 5.43 m/s after the collision.
2) The recoil velocity of the launcher can be determined by applying the principle of conservation of momentum.
The momentum of the potato can be calculated as:
Momentum of potato = mass of potato * velocity of potato = (9 kg) * (283 m/s) = 2547 kg·m/s
According to the conservation of momentum, the total momentum before and after the launch should be equal.
Since the cannon is initially at rest, its momentum before the launch is zero.
After the launch, the cannon and the potato move in opposite directions with different velocities. Let's assume the recoil velocity of the launcher is v.
The total momentum after the launch is the sum of the momentum of the potato and the momentum of the cannon, which can be expressed as:
Total momentum after = Momentum of potato + (mass of cannon * recoil velocity)
According to the conservation of momentum, the total momentum before and after the launch should be equal. Therefore, we can set up an equation:
Momentum of potato = mass of cannon * recoil velocity
Substituting the given values:
2547 kg·m/s = (155 kg) * v
Now, we can solve for the recoil velocity (v):
v = 2547 kg·m/s / 155 kg ≈ 16.44 m/s
Therefore, the recoil velocity of the cannon is approximately 16.44 m/s.
3) To determine the velocity of the truck and car after the collision, we can apply the principle of conservation of momentum.
The momentum of an object can be calculated by multiplying its mass by its velocity. Therefore, the momentum of the truck before the collision can be calculated as:
Momentum of truck = mass of truck * velocity of truck = (994 kg) * (17 m/s) = 16,898 kg·m/s
The momentum of the car before the collision can be calculated as:
Momentum of car = mass of car * velocity of car = (700 kg) * (5 m/s) = 3,500 kg·m/s
After the collision, the two vehicles stick together, so they have a common final velocity, let's call it v.
The total momentum after the collision is the sum of the momenta of the truck and the car, which can be expressed as:
Total momentum after = (mass of truck + mass of car) * final velocity = (994 kg + 700 kg) * v
According to the conservation of momentum, the total momentum before and after the collision should be equal. Therefore, we can set up an equation:
16,898 kg·m/s + 3,500 kg·m/s = (994 kg + 700 kg) * v
Now we can solve for the final velocity (v):
v = (16,898 kg·m/s + 3,500 kg·m/s) / (994 kg + 700 kg) ≈ 16.62 m/s
Therefore, the velocity of the truck and car after the collision is approximately 16.62 m/s.
4) To determine the recoil velocity of the rifle, we can again apply the principle of conservation of momentum.
The momentum of an object can be calculated by multiplying its mass by its velocity. Therefore, the momentum of the bullet can be calculated as:
Momentum of bullet = mass of bullet * velocity of bullet = (0.3 kg) * (267.9 m/s) = 80.37 kg·m/s
According to the conservation of momentum, the total momentum before and after the shot should be equal.
Since Steve is loosely holding the rifle, we can assume that the mass of the rifle is negligible compared to that of the bullet. Therefore, the momentum before the shot is essentially zero.
After the shot, the bullet moves in one direction with a specific velocity, and the rifle moves in the opposite direction with a recoil velocity, let's call it v.
The total momentum after the shot is the sum of the momentum of the bullet and the momentum of the rifle, which can be expressed as:
Total momentum after = Momentum of bullet + (mass of rifle * recoil velocity)
According to the conservation of momentum, the total momentum before and after the shot should be equal. Therefore, we can set up an equation:
Momentum of bullet = mass of rifle * recoil velocity
Substituting the given values:
80.37 kg·m/s = (2.4 kg) * v
Now, we can solve for the recoil velocity (v):
v = 80.37 kg·m/s / 2.4 kg ≈ 33.49 m/s
Therefore, the recoil velocity of the rifle is approximately 33.49 m/s.