Two cars, one of mass 1300 kg, and the second of mass 2200 kg, are moving at right angles to each other when they collide and stick together. he initial velocity of the first car is 14 m/s in the positive x direction and that of the second car is 18 m/s in the positive y

direction.
What is the magnitude of the velocity of the
wreckage of the two cars immediately after the

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momentum after = momentum before
momentum is a vector
so
momentum in the x direction after = momentum in the x direction before
and
momentum in the y direction after = momentum in the y direction after.

mass is conserved. Total mass after = total mass before

To find the magnitude of the velocity of the wreckage immediately after the collision, we can use the law of conservation of momentum.

Step 1: Calculate the momentum of each car before the collision.
Momentum is calculated by multiplying the mass of an object by its velocity.
Momentum of the first car (P1) = mass of first car (m1) * velocity of first car (v1)
P1 = 1300 kg * 14 m/s

Momentum of the second car (P2) = mass of second car (m2) * velocity of second car (v2)
P2 = 2200 kg * 18 m/s

Step 2: Calculate the total momentum before the collision.
The total momentum before the collision is the sum of the individual momenta of the two cars.
Total momentum before collision = P1 + P2

Step 3: Calculate the mass of the wreckage.
Since the two cars stick together after the collision, the mass of the wreckage is the sum of the masses of the two cars.
Mass of the wreckage = mass of first car + mass of second car

Step 4: Calculate the velocity of the wreckage.
With the total momentum and mass of the wreckage, we can calculate its velocity.
Velocity of the wreckage = total momentum before collision / mass of the wreckage

Step 5: Find the magnitude of the velocity of the wreckage.
The magnitude of velocity is the absolute value of the velocity.
Magnitude of velocity of the wreckage = absolute value of velocity of the wreckage

Now let's perform the calculations:

Step 1:
P1 = 1300 kg * 14 m/s = 18200 kg·m/s
P2 = 2200 kg * 18 m/s = 39600 kg·m/s

Step 2:
Total momentum before collision = 18200 kg·m/s + 39600 kg·m/s = 57800 kg·m/s

Step 3:
Mass of the wreckage = 1300 kg + 2200 kg = 3500 kg

Step 4:
Velocity of the wreckage = 57800 kg·m/s / 3500 kg = 16.514 m/s

Step 5:
Magnitude of velocity of the wreckage = |16.514 m/s| ≈ 16.514 m/s

Therefore, the magnitude of the velocity of the wreckage immediately after the collision is approximately 16.514 m/s.

To find the magnitude of the velocity of the wreckage immediately after the collision, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.

The momentum of an object is calculated by multiplying its mass by its velocity. Therefore, the initial momentum of the first car in the x direction is calculated as follows:

Momentum of the first car in x direction = mass of the first car × velocity of the first car in x direction
= 1300 kg × 14 m/s
= 18200 kg·m/s

Similarly, the initial momentum of the second car in the y direction is calculated as follows:

Momentum of the second car in y direction = mass of the second car × velocity of the second car in y direction
= 2200 kg × 18 m/s
= 39600 kg·m/s

Since the two cars stick together after the collision, we can consider them as one body with a combined mass of 1300 kg + 2200 kg = 3500 kg. The velocity of the wreckage, which is the final velocity after the collision, can be calculated as the ratio of the total momentum to the total mass:

Velocity of wreckage = (momentum of the first car in x direction + momentum of the second car in y direction) / total mass
= (18200 kg·m/s + 39600 kg·m/s) / 3500 kg
= 57800 kg·m/s / 3500 kg
= 16.514 m/s

So, the magnitude of the velocity of the wreckage immediately after the collision is approximately 16.514 m/s.