Final answer:
To find the truck's velocity, we used the law of conservation of momentum, considering the combined final velocity to be zero after the collision. With the given masses and the car's speed, the truck's velocity was calculated to be 3.02 m/s in the opposite direction to fulfill the conservation of momentum.
Step-by-step explanation:
The velocity of the truck before a collision where both vehicles stick together and stop immediately can be found using the law of conservation of momentum. According to this law, the total momentum before the collision must equal the total momentum after the collision, provided no external forces are acting on the system. In a head-on collision where the final velocity of both vehicles is zero, the initial momentum of both vehicles is also zero. This can be expressed by the equation:
m1⋅v1 + m2⋅v2 = (m1 + m2)⋅v_final
Given that the car has a mass (m1) of 1300 kg and travels at 100 km/h (which is approximately 27.78 m/s) and the truck has a mass (m2) of 12000 kg with an unknown velocity (v2), we can rearrange this equation to solve for v2, the truck's velocity.
Since we know that v_final = 0 (the vehicles stop), the equation becomes:
1300 kg ⋅ 27.78 m/s + 12000 kg ⋅ v2 = 0
Solving for v2:
12000 kg ⋅ v2 = -1300 kg ⋅ 27.78 m/s
v2 = -(1300 kg ⋅ 27.78 m/s) / 12000 kg
v2 = -3.02 m/s (negative sign indicates opposite direction)
In conclusion, for the vehicles to stick together and stop immediately upon collision, the truck must have been moving at 3.02 m/s in the opposite direction.