A car x of mass 1000kg traveling at a speed of 20m/s in the direction due east collides head on with a car y of mass1500kg traveling at 15m/s in a direction due west . If the two cars stick together find their common velocity after collision.
conserve momentum
If east is the + direction, then we have
1000(+20) + 1500(-15) = (1000+1500)v
Now just solve for v.
To find the common velocity of the two cars after the collision, 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.
Momentum is defined as the product of mass and velocity. Therefore, the momentum of car x before the collision is given by:
Momentum (x) = Mass (x) * Velocity (x)
Momentum (x) = 1000 kg * 20 m/s = 20,000 kg·m/s (due east)
The momentum of car y before the collision is given by:
Momentum (y) = Mass (y) * Velocity (y)
Momentum (y) = 1500 kg * (-15 m/s) = -22,500 kg·m/s (due west)
As the two cars stick together after the collision, their total mass will be the sum of their individual masses, i.e., 1000 kg + 1500 kg = 2500 kg.
Let's assume the common velocity after the collision is V (due east).
Now, we can write the conservation of momentum equation as:
Total Initial Momentum = Total Final Momentum
Momentum (x) + Momentum (y) = Total Mass * Common Velocity
20,000 kg·m/s + (-22,500 kg·m/s) = 2500 kg * V
-2,500 kg·m/s = 2500 kg * V
Dividing both sides by 2500 kg:
-2,500 kg·m/s / 2500 kg = V
-1 m/s = V
Therefore, the common velocity of the two cars after the collision is -1 m/s (due west).