Final answer:
By using the conservation of momentum, the final direction of motion of the combined car and truck after the collision is 45 degrees relative to east. The calculation uses the total momentums in the eastward and northward directions, both being 80000 kg*m/s, and the fact that the collision was perfectly inelastic.
Step-by-step explanation:
The subject of this question is Physics, particularly the topic of momentum and collisions. Focusing on the situation described, we have a small car with mass 2000kg is moving east with a velocity 40 m/s, and it gets hit and sticks to a truck, with mass 10000kg, which was originally moving north with velocity 8 m/s. To find the direction of motion after the collision, we apply the law of conservation of momentum since the intersection is icy and therefore no external frictional forces are acting on the system.
First, we calculate the total momentum in the eastward direction (x-direction) before the collision:
- Px_total = m_car * v_car = 2000kg * 40 m/s = 80000 kg*m/s
Then the total momentum in the northward direction (y-direction) before the collision:
- Py_total = m_truck * v_truck = 10000kg * 8 m/s = 80000 kg*m/s
After the collision, the car and the truck stick together, so their combined mass is 2000kg + 10000kg = 12000kg. Since the collision is perfectly inelastic, momentum is conserved in both directions:
- Px_total_after = Px_total
- Py_total_after = Py_total
To find the resultant velocity of the combined masses, we use the momenta in both directions:
- Velocity_x = Px_total_after / combined_mass = 80000 kg*m/s / 12000kg = 6.67 m/s
- Velocity_y = Py_total_after / combined_mass = 80000 kg*m/s / 12000kg = 6.67 m/s
Now, we can calculate the final velocity vector of the masses stuck together using the Pythagorean theorem:
- Velocity_total = √(Velocity_x² + Velocity_y²) = √(6.67² + 6.67²) m/s
And we use the inverse tangent function to find the direction of this combined velocity:
- Direction = atan(Velocity_y / Velocity_x) = atan(6.67 m/s / 6.67 m/s)
This will give us the angle relative to the east after the collision, which will be 45 degrees (since the magnitudes of the velocities in x and y direction are equal).