Based upon the problem statement, we can deduce that this is a physics problem related to the conservation of momentum. We will solve for the magnitude and direction of the final velocity of the two cars after they have collided and stuck together.
The cars are moving in 2-dimensional space. For simplicity, we will follow the conventional notation of defining east as 0 degrees, north as 90 degrees, west as 180 degrees, and south as 270 degrees. We are also going to use these directions clockwise.
Step 1: Define the properties of the cars
Car 1:
- Mass (m1) = 1450 kg
- Speed (v1) = 7.00 m/s
- Direction = 270 degrees (south)
Car 2:
- Mass (m2) = 800 kg
- Speed (v2) = 25.0 m/s
- Direction = 180 degrees (west)
Step 2: Convert the speeds and direction into vectors
For this, we use the cosine and sine functions of the angle to find the velocities in the x and y directions respectively. This gives us:
- Velocity of car 1 = [7*cos(270°), 7*sin(270°)]
- Velocity of car 2 = [25*cos(180°), 25*sin(180°)]
Step 3: Solve for the combined velocity using the conservation of momentum
The conservation of momentum states that the total momentum before the collision is equal to the total momentum after the collision.
Hence, (m1*v1 + m2*v2) = (m1+m2)v
Substituting the masses and velocities of both cars, we solve this equation to get the combined velocity:
- Combined Velocity = (First car's mass x first car's velocity + second car's mass x second car's velocity)/(m1 + m2)
Step 4: Find the magnitude and direction of the combined velocity
The magnitude can be found using the Euclidean norm of the combined velocity vector. The direction can be determined by calculating the arctangent of the ratio of the 'y' component to the 'x' component of the combined velocity vector. This gives us results in radians which we then convert to degrees. If the direction value obtained is less than 0, we add 360 to it to adjust for the direction being measured counter-clockwise from east.
Finally, the final velocity (magnitude and direction) of the cars after the collision is approximately 9.97 m/s and 206.91 degrees. Thus, the cars would be moving approximately towards the southwest.