A 1500-kg car moving north at 27.0 m/s is struck by a 2165-kg car moving east at 13.0 m/s. The cars are stuck together. How fast and in what direction do they move immediately after the collision?

1. Degree north of east?
2. M/S?

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To solve this problem, we can use the principles of momentum conservation. The total momentum before the collision is equal to the total momentum after the collision.

Step 1: Calculate the initial momenta of the two cars.
The momentum of a body is given by the product of its mass and velocity.
For the first car moving north:
Momentum_1 = mass_1 * velocity_1 = 1500 kg * 27.0 m/s = 40,500 kg·m/s
For the second car moving east:
Momentum_2 = mass_2 * velocity_2 = 2165 kg * 13.0 m/s = 28,145 kg·m/s

Step 2: Calculate the resultant momentum.
To determine the direction and speed of the cars immediately after the collision, we need to calculate the resultant momentum.
In a collision, the momentum is conserved, meaning the total momentum after the collision is equal to the total momentum before.
Resultant momentum = Momentum_1 + Momentum_2
Resultant momentum = 40,500 kg·m/s + 28,145 kg·m/s = 68,645 kg·m/s

Step 3: Calculate the velocity and direction of the cars after the collision.
To calculate the velocity and direction, we will divide the resultant momentum by the total mass of the system.
Total mass = mass_1 + mass_2
Total mass = 1500 kg + 2165 kg = 3665 kg

Velocity after the collision = Resultant momentum / Total mass
Velocity after the collision = 68,645 kg·m/s / 3665 kg = 18.73 m/s

The direction of the velocity can be found using trigonometry. We have the North and East components of the velocity, so we can use these to find the angle.
Angle = arctan(North velocity component / East velocity component)
Angle = arctan(40,500 kg·m/s / 28,145 kg·m/s)
Angle = arctan(1.44)

Calculating the angle, we find that it is roughly 54.1 degrees.

Now, let's answer the specific questions asked:

1. The resulting direction of motion after the collision can be described as 54.1 degrees north of east.
2. The resulting speed of the cars after the collision is 18.73 m/s.