A truck of mass 1.3 X 104 kg, travelling at 9.0 × 10' km/h [N], collides with a car of mass 1.1 X 103 kg, travelling at 3.0 X 10' km/h [N]. If the collision is completely inelastic, what are the magnitude and direction of the velocity of the vehicles immedi ately after the collision?
To solve this problem, we need to first use the principle of conservation of momentum. In an inelastic collision, the total momentum before the collision is equal to the total momentum after the collision.
Let's denote the velocity of the truck before the collision as v1 and the velocity of the car before the collision as v2. The total initial momentum of the system is:
Initial momentum = (mass of truck * velocity of truck) + (mass of car * velocity of car)
= (1.3 X 10^4 kg * 9.0 X 10^3 km/h) + (1.1 X 10^3 kg * 3.0 X 10^3 km/h)
Now, since the collision is completely inelastic, the two vehicles stick together after the collision. Let's denote the velocity of the combined vehicles after the collision as V.
The final momentum of the system is:
Final momentum = (total mass * final velocity)
= ((1.3 X 10^4 kg + 1.1 X 10^3 kg) * V)
Now, we can set the initial momentum equal to the final momentum and solve for V:
(1.3 X 10^4 kg * 9.0 X 10^3 km/h) + (1.1 X 10^3 kg * 3.0 X 10^3 km/h) = (1.3 X 10^4 kg + 1.1 X 10^3 kg) * V
Solving for V, we get:
V = ((1.3 X 10^4 kg * 9.0 X 10^3 km/h) + (1.1 X 10^3 kg * 3.0 X 10^3 km/h)) / (1.3 X 10^4 kg + 1.1 X 10^3 kg)
V = (1.17 X 10^8 kg*km/h + 3.3 X 10^6 kg*km/h) / 1.43 X 10^4 kg
V = 8.31 X 10^3 km/h
Therefore, the magnitude of the velocity of the combined vehicles immediately after the collision is 8.31 X 10^3 km/h. Since the collision is completely inelastic, the direction of the velocity will be in the direction of the initial motion of the truck.