A 1100- kg car collides with a 1500- kg car that was initially at rest at the origin of an x-y coordinate system. After the collision, the lighter car moves at 20.0 km/h in a direction of 35 o with respect to the positive x axis. The heavier car moves at 23 km/h at -50 o with respect to the positive x axis.

What was the initial speed of the lighter car (in km/h)?
What was the initial direction (as measured counterclockwise from the x-axis)?

To find the initial speed of the lighter car, we need to 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, p, is given by the formula: p = m * v, where m is the mass of the object and v is its velocity.

Let's denote the initial velocity of the lighter car as V1, and the initial velocity of the heavier car as V2. After the collision, the lighter car moves at a velocity of 20.0 km/h, and the heavier car moves at a velocity of 23 km/h.

Using the conservation of momentum, we can set up the following equation:

(mass of lighter car * V1) + (mass of heavier car * V2) = (mass of lighter car * velocity of lighter car) + (mass of heavier car * velocity of heavier car)

Substituting the given values:

(1100 kg * V1) + (1500 kg * 0) = (1100 kg * 20.0 km/h) + (1500 kg * 23 km/h)

Where we set the velocity of the heavier car as 0 because it was initially at rest.

Simplifying the equation:

1100 kg * V1 = 1100 kg * 20.0 km/h + 1500 kg * 23 km/h

The masses of the two cars cancel out, so we are left with:

V1 = 20.0 km/h + (1500/1100) * 23 km/h

Calculating the right side of the equation:

V1 = 20.0 km/h + (1.3636 * 23 km/h)
V1 = 20.0 km/h + 31.3636 km/h
V1 = 51.3636 km/h

Therefore, the initial speed of the lighter car is approximately 51.36 km/h.

To find the initial direction counterclockwise from the x-axis, we can use trigonometry. The given information tells us that the lighter car moves at 20.0 km/h in a direction of 35 degrees with respect to the positive x-axis.

The initial direction counterclockwise from the x-axis can be found by subtracting the given angle from 90 degrees. In our case, it would be:

Initial direction = 90 degrees - 35 degrees
Initial direction = 55 degrees

Therefore, the initial direction of the lighter car is approximately 55 degrees counterclockwise from the x-axis.