A lorry of mass 12,000kg traveling at a velocity of 15 m/s crashes into the back of a moving car of mass 1500kg, traveling at a velocity of 5 m/s. The vehicles move together after the impact. Calculate their velocity.
13.9m/s
To find the final velocity of the vehicles after the impact, we 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. Therefore, the momentum of the lorry before the collision is:
Momentum of lorry before = mass of lorry × velocity of lorry = 12,000 kg × 15 m/s = 180,000 kg·m/s.
The momentum of the car before the collision is:
Momentum of car before = mass of car × velocity of car = 1,500 kg × 5 m/s = 7,500 kg·m/s.
The total momentum before the collision is the sum of the individual momenta:
Total momentum before = Momentum of lorry before + Momentum of car before
= 180,000 kg·m/s + 7,500 kg·m/s
= 187,500 kg·m/s.
Let's assume that the vehicles move together with a final velocity of v m/s after the impact. The total momentum after the collision is the sum of the individual momenta:
Total momentum after = (mass of lorry + mass of car) × final velocity
= (12,000 kg + 1,500 kg) × v
= 13,500 kg × v.
According to the principle of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision:
Total momentum before = Total momentum after
187,500 kg·m/s = 13,500 kg × v.
Now, we can solve the equation to find the final velocity, v:
v = 187,500 kg·m/s / 13,500 kg
v ≈ 13.89 m/s.
Therefore, after the impact, the vehicles will move together with a velocity of approximately 13.89 m/s.
To calculate the final velocity of the vehicles, we need to apply 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.
Momentum is the product of an object's mass and its velocity. The equation for momentum is:
momentum = mass × velocity
For the lorry:
mass1 = 12,000 kg
velocity1 = 15 m/s
For the car:
mass2 = 1,500 kg
velocity2 = 5 m/s
The total momentum before the collision is given by the sum of the individual momenta of the lorry and the car:
initial momentum = (mass1 × velocity1) + (mass2 × velocity2)
The total momentum after the collision is given by the sum of their individual momenta, which remain the same:
final momentum = (mass1 + mass2) × final velocity
Since the vehicles move together after the impact, their final velocity is the same. Therefore, we can equate the initial and final momentum equations:
(mass1 × velocity1) + (mass2 × velocity2) = (mass1 + mass2) × final velocity
Plugging in the given values:
(12,000 kg × 15 m/s) + (1,500 kg × 5 m/s) = (12,000 kg + 1,500 kg) × final velocity
Simplifying:
180,000 kg·m/s + 7,500 kg·m/s = 13,500 kg × final velocity
187,500 kg·m/s = 13,500 kg × final velocity
Now we can solve for the final velocity:
final velocity = 187,500 kg·m/s / 13,500 kg
final velocity ≈ 13.8889 m/s
Therefore, the final velocity of the vehicles after the collision is approximately 13.8889 m/s.