To solve this problem, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision should be equal to the total momentum after the collision.
Let's calculate the momentum of the car and the truck before the collision separately.
The momentum of an object is given by the product of its mass (m) and its velocity (v).
The momentum (p) is calculated using the formula:
p = m * v
Let's calculate the momentum of the car before the collision:
Mass of the car (m1) = 1000 kg
Velocity of the car (v1) = 13 m/s
Momentum of the car before the collision (p1) = m1 * v1
p1 = 1000 kg * 13 m/s
p1 = 13,000 kg·m/s (North)
Similarly, let's calculate the momentum of the truck before the collision:
Mass of the truck (m2) = 2000 kg
Velocity of the truck (v2) = -17 m/s (since it is south, we take negative velocity)
Momentum of the truck before the collision (p2) = m2 * v2
p2 = 2000 kg * (-17 m/s)
p2 = -34,000 kg·m/s (South)
Now, let's calculate the momentum after the collision.
The equation for conservation of momentum can be written as:
p1 + p2 = p1' + p2'
Where p1' and p2' represent the momentums of the car and the truck immediately after the collision, respectively.
Given that the velocity of the car immediately after the collision is 11 m/s (South), we can calculate its momentum:
Mass of the car (m1') = 1000 kg
Velocity of the car (v1') = -11 m/s (South)
Momentum of the car after the collision (p1') = m1' * v1'
p1' = 1000 kg * (-11 m/s)
p1' = -11,000 kg·m/s (South)
Now, let's substitute the values into the conservation of momentum equation to solve for the momentum of the truck after the collision:
13,000 kg·m/s (North) + (-34,000 kg·m/s (South)) = -11,000 kg·m/s (South) + p2'
Subtracting 13,000 kg·m/s (North) from both sides:
-34,000 kg·m/s (South) = -11,000 kg·m/s (South) + p2' - 13,000 kg·m/s (North)
Combining the South terms on the right side:
-34,000 kg·m/s - (-11,000 kg·m/s) = p2' - 13,000 kg·m/s
Simplifying the left side:
-34,000 kg·m/s + 11,000 kg·m/s = p2' - 13,000 kg·m/s
-23,000 kg·m/s = p2' - 13,000 kg·m/s
Adding 13,000 kg·m/s to both sides:
-23,000 kg·m/s + 13,000 kg·m/s = p2'
-10,000 kg·m/s = p2'
Therefore, the momentum of the truck immediately after the collision is -10,000 kg·m/s. The negative sign indicates that the truck is still traveling south.
To find the velocity of the truck immediately after the collision, we can divide its momentum by its mass:
Momentum of the truck after the collision (p2') = -10,000 kg·m/s
Mass of the truck (m2) = 2000 kg
Velocity of the truck after the collision (v2') = p2' / m2
v2' = (-10,000 kg·m/s) / (2000 kg)
v2' = -5 m/s
Therefore, the velocity of the truck immediately after the collision is 5 m/s in the south direction.