what about a 5,000 kg truck rear-ends a 1200 kg car that has been traveling at 13 m/s, causing the truck to slow down from 14 m/s to 12 m/s and the car to speed up. What is the final velocity?
again, this should not be an elastic collision,
momentum change...
5000*(14-12)+1200(13+v)=0
(ie, the net change of momentum is zero.)
Solve for v, the final velocity of the car.
when I solve for that, i got -8.5 which can't be possible seeing the car started at 13.
did i do something wrong?
Arrrggggg.
change momentum = mass(vf-vi)!!!!
5000(12-14)+1200(V-13)=0
V-13=10000/1200
V=13+8.5=21.5m/s
got it! thank you so much!!
To find the final velocity of the car after being rear-ended, we can use the conservation of momentum principle, 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. We can express momentum using the equation:
Momentum = mass × velocity
Before the collision, the momentum of the car (m1v1) is:
Momentum of car = 1200 kg × 13 m/s
After the collision, the momentum of the car (m1vf1) and truck (m2vf2) together is equal to the total momentum before the collision:
m1v1 + m2v2 = m1vf1 + m2vf2
Substituting the given values, we get:
(1200 kg × 13 m/s) + (5000 kg × 14 m/s) = (1200 kg × vf1) + (5000 kg × 12 m/s)
Now, let's simplify and solve the equation to find the final velocity (vf1) of the car:
15600 kg·m/s + 70000 kg·m/s = 1200 kg × vf1 + 60000 kg·m/s
85600 kg·m/s = 1200 kg × vf1 + 60000 kg·m/s
25600 kg·m/s = 1200 kg × vf1
vf1 = 25600 kg·m/s ÷ 1200 kg
vf1 = 21.33 m/s (rounded to two decimal places)
Therefore, the final velocity of the car after being rear-ended is approximately 21.33 m/s.