A 1400 kg car traveling at 15.5 m/s to the
south collides with a 4100 kg truck that is
initially at rest at a stoplight. The car and
truck stick together and move together after
the collision.
What is the final velocity of the two-vehicle
mass?
20.0
To find the final velocity of the two-vehicle mass after the collision, you can use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
The momentum of an object is calculated by multiplying its mass by its velocity. Let's denote the mass of the car as m1 and the mass of the truck as m2. The initial velocity of the car is v1 and the initial velocity of the truck is v2, which is 0 since it is initially at rest.
The momentum before the collision can be calculated as:
Initial momentum of car = m1 * v1
Initial momentum of truck = m2 * v2 = 0
The total initial momentum is equal to the sum of the individual momenta:
Total initial momentum = Initial momentum of car + Initial momentum of truck
After the collision, the two vehicles stick together and move with a common final velocity, which we can denote as vf. Since they move together, their total mass is equal to the sum of their individual masses:
Total mass after collision = m1 + m2
The total momentum after the collision is calculated as:
Total momentum after collision = Total mass after collision * vf
According to the conservation of momentum principle, the total initial momentum is equal to the total momentum after the collision:
Total initial momentum = Total momentum after collision
We can set up an equation using these principles:
m1 * v1 = (m1 + m2) * vf
Plugging in the given values:
m1 = 1400 kg
v1 = 15.5 m/s
m2 = 4100 kg
1400 kg * 15.5 m/s = (1400 kg + 4100 kg) * vf
Now we can solve for vf:
(1400 kg * 15.5 m/s) / (1400 kg + 4100 kg) = vf
Calculating this expression gives us:
vf = 5.00 m/s
Therefore, the final velocity of the two-vehicle mass after the collision is 5.00 m/s to the south.