a 12,000 kg truck is moving right at 22 m/s collides with and sticks to a 1200 kg car moving to the right at 16 m/s. With what speed do the two vehicles move after the collision and in what direction?
everything is moving right so will continue to do so
final momentum = initial momentum
initial momentum =12,000*22 + 1200*16
final momentum = (12,000+1,200) v
To determine the final velocity of the two vehicles after the collision, we can use the law of conservation of momentum, which states that 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 velocity of the truck before the collision as v1, the velocity of the car before the collision as v2, the final velocity of the two vehicles after the collision as vf, and the combined mass of the truck and car as M.
Momentum before collision = Momentum after collision
(Mass of truck × Velocity of truck before collision) + (Mass of car × Velocity of car before collision) = (Mass of truck + Mass of car) × Velocity of the combined vehicles after collision
(12000 kg × v1) + (1200 kg × v2) = (12000 kg + 1200 kg) × vf
Now we have to solve for the final velocity (vf).
Using the information given:
Mass of truck (m1) = 12000 kg
Velocity of truck before collision (v1) = 22 m/s
Mass of car (m2) = 1200 kg
Velocity of car before collision (v2) = 16 m/s
Substituting the values into the equation:
(12000 kg × 22 m/s) + (1200 kg × 16 m/s) = (12000 kg + 1200 kg) × vf
264000 kg·m/s + 19200 kg·m/s = 13200 kg × vf
283200 kg·m/s = 13200 kg × vf
Dividing both sides of the equation by 13200 kg:
vf = 283200 kg·m/s ÷ 13200 kg
vf ≈ 21.45 m/s
Therefore, the two vehicles move with a final velocity of approximately 21.45 m/s to the right after the collision.