A 1250 kg car rams into the back of a slower moving truck having a mass of 2500 kg. During the collision the two vehicles become entangled so that they move off together afterward. If before the collision the car was going 20 m/s and the truck was going 14 m/s, what was their final velocity?
m1=1250 kg, m2=2500 kg,
v1=20 m/s, v2 =14 m/s.
u=?
m1•v1+m2•v2= (m1+m2)u
Solve for ‘u’
thank you so much!
To find the final velocity of the two vehicles after the collision, we can use the principle of conservation of momentum. According to this principle, the total momentum of a system remains constant before and after a collision, assuming no external forces are involved.
The momentum of an object is defined as the product of its mass and velocity. Mathematically, momentum (p) can be calculated as:
p = mass × velocity
Let's denote the mass of the car as m1 (1250 kg) and its velocity before the collision as v1 (20 m/s). Similarly, we denote the mass of the truck as m2 (2500 kg) and its velocity before the collision as v2 (14 m/s). We can calculate the initial momentum of the car (p1) and the initial momentum of the truck (p2) as follows:
p1 = m1 × v1
p2 = m2 × v2
During the collision, the two vehicles become entangled, meaning they move together as one system afterward. Let's denote the final velocity of the combined system as vf. The total mass of the combined system is the sum of the masses of the car and the truck, and the total momentum of the system after the collision will be the sum of the initial momenta of the individual vehicles. Mathematically, we can represent this as:
p1 + p2 = (m1 + m2) × vf
Now, we can plug in the given values and solve for vf:
p1 = (1250 kg) × (20 m/s) = 25,000 kg·m/s
p2 = (2500 kg) × (14 m/s) = 35,000 kg·m/s
25,000 kg·m/s + 35,000 kg·m/s = (1250 kg + 2500 kg) × vf
60,000 kg·m/s = 3750 kg × vf
vf = 60,000 kg·m/s ÷ 3750 kg
vf ≈ 16 m/s
Therefore, the final velocity of the car and the truck combined after the collision is approximately 16 m/s.