Final answer:
Using the conservation of momentum, the velocity of the entangled 2400 kg mass after the collision, with the 500 kg car striking a 1900 kg truck at 23 m/s, is 4.79 m/s to the north.
Step-by-step explanation:
To calculate the velocity of the entangled mass after the collision, we use the conservation of momentum, which states that the total momentum before the collision is equal to the total momentum after the collision. For our scenario, we have a 1900 kg truck at rest and a 500 kg car moving northward at 23 m/s. Initially, the truck's momentum is 0 kg·m/s because it is not moving. The car's momentum is the product of its mass and velocity, so 500 kg × 23 m/s = 11500 kg·m/s north.
Since the two vehicles become entangled, we have a single mass after the collision, which is the sum of both masses, 1900 kg + 500 kg = 2400 kg. Using the conservation of momentum, we find that the total momentum before the collision (11500 kg·m/s) will be the same after the collision. We use the formula:
m
combined
× v
combined
= p
total
, where
v
combined
is the velocity of the entangled mass.
Thus:
2400 kg × vcombined = 11500 kg·m/s
Dividing both sides by 2400 kg, we get:
vcombined = 11500 kg·m/s / 2400 kg
vcombined = 4.79 m/s to the north.
The velocity of the entangled mass after the collision is 4.79 m/s to the north.