A blue car with mass mc = 410.0 kg is moving east with a speed of vc = 23.0 m/s and collides with a purple truck with mass mt = 1248.0 kg that is moving south with a speed of vt = 10.0 m/s . The two collide and lock together after the collision.

1)What is the magnitude of the initial momentum of the car?
2)What is the magnitude of the initial momentum of the truck?
3)What is the angle that the car-truck combination travel after the collision? (give your answer as an angle South of East)
4)What is the magnitude of the momentum of the car-truck combination immediately after the collision?
5)What is the speed of the car-truck combination immediately after the collision?

1. Mc*Vc = 410*23 = 9430.

2. Mt*Vt = 1248*10 = 12,480.

3. Tan A = Mt*Vt/Mc*Vc = (-12,480)/9430
= -1.32344.
A = -52.9o. = 52.9o S. of E.

4. (-12,480)/sin(-52.9) = 15,547

5. Mc*Vc + Mt*Vt = Mc*V + Mt*V.
9430 - 12,480i = 410V + 1248V.
15,547[-52.9o] = 1658V.
V = 9.44m/s[-52.9o] = 52.9o S. of E.

To solve this problem, we can use the principles of momentum conservation.

1) To find the magnitude of the initial momentum of the car, we need to multiply its mass (mc = 410.0 kg) by its velocity (vc = 23.0 m/s):
Initial momentum of the car = mc * vc = 410.0 kg * 23.0 m/s = 9430.0 kg·m/s

2) Similarly, to find the magnitude of the initial momentum of the truck, we multiply its mass (mt = 1248.0 kg) by its velocity (vt = 10.0 m/s):
Initial momentum of the truck = mt * vt = 1248.0 kg * 10.0 m/s = 12480.0 kg·m/s

3) After the collision, the car and truck lock together and move in a certain direction. To find the resulting angle of motion, we can use trigonometry. The angle can be determined using the following equation:
tan(θ) = mc * vc / mt * vt

Substituting the given values, we get:
tan(θ) = 410.0 kg * 23.0 m/s / 1248.0 kg * 10.0 m/s
tan(θ) = 9430.0 / 12480.0
θ = atan(9430.0 / 12480.0)

Using a calculator, we find θ ≈ 37.1 degrees.

4) After the collision, the car and truck lock together, so their combined mass is (mc + mt = 410.0 kg + 1248.0 kg = 1658.0 kg). The momentum of the car-truck combination is equal to its mass multiplied by its velocity. Since the car and truck have locked together, they have the same velocity:
Momentum of the car-truck combination = (mc + mt) * velocity

Substituting the given value of velocity as 23.0 m/s, we get:
Momentum of the car-truck combination = 1658.0 kg * 23.0 m/s = 38134.0 kg·m/s

5) The speed of the car-truck combination is the magnitude of its velocity vector. Since the car and truck have locked together after the collision, they have the same speed:
Speed of the car-truck combination = velocity = 23.0 m/s

So, the answers to the given questions are:
1) The magnitude of the initial momentum of the car is 9430.0 kg·m/s.
2) The magnitude of the initial momentum of the truck is 12480.0 kg·m/s.
3) The angle that the car-truck combination travels after the collision is approximately 37.1 degrees south of east.
4) The magnitude of the momentum of the car-truck combination immediately after the collision is 38134.0 kg·m/s.
5) The speed of the car-truck combination immediately after the collision is 23.0 m/s.

To answer these questions, we need to use the concept of conservation of momentum. According to this principle, the total momentum of a system remains constant before and after a collision, provided no external forces are involved.

Here's how we can find the answers to the questions:

1) The magnitude of the initial momentum of the car (mc) is given by the product of its mass and velocity, p = mc * vc.
Therefore, p_car = 410.0 kg * 23.0 m/s.

2) Similarly, the magnitude of the initial momentum of the truck (mt) is given by the product of its mass and velocity, p = mt * vt.
Therefore, p_truck = 1248.0 kg * 10.0 m/s.

3) To find the angle at which the car-truck combination travels after the collision, we can use the concept of vectors.
Let's assume the positive x-direction is east and the positive y-direction is north.
The momentum of the car-truck combination after the collision can be represented as a vector sum of the individual momenta.
The car moves in the east direction, and the truck moves in the south direction.
Therefore, the angle it travels will be south of east.

4) Since momentum is conserved, the magnitude of the momentum of the car-truck combination immediately after the collision is equal to the sum of the individual momenta before the collision.
Therefore, p_car-truck = p_car + p_truck.

5) The speed of the car-truck combination immediately after the collision is the magnitude of its momentum divided by the total mass.
speed = p_car-truck / (mc + mt).

By using the given values for mass and velocity, we can substitute them into the equations to calculate the results.

sfsadf