1. Car A, with mass of 1250 kg, is travelling at 30 m/s to the east. Car B is a truck with mass of 2000 kg, travelling to the west at 25 m/s. Assume these two vehicles experience an inelastic collision but do not stick together, and Car A goes off 10 m/s to the west. What will be the resulting velocity of Car B?
change in momentum of car A = 1250 (40) = 50,000 toward the west
so change in momentum of car B is 50,000 toward the east
50,000 = 2000 (east velocity - -25)
25 = east velocity + 25
east velocity = 0
stopped it dead in the water :)
To find the resulting velocity of Car B after the collision, we can use the principle of conservation of momentum. In an inelastic collision, the total momentum before the collision is equal to the total momentum after the collision.
Let's break down the problem and calculate the initial momentum and the final momentum separately.
Step 1: Calculate the initial momentum.
The initial momentum can be calculated using the formula:
Initial momentum = mass × velocity
For Car A:
Mass of Car A = 1250 kg
Velocity of Car A = 30 m/s to the east
Momentum of Car A = 1250 kg × 30 m/s = 37500 kg·m/s to the east
For Car B:
Mass of Car B = 2000 kg
Velocity of Car B = 25 m/s to the west
Momentum of Car B = 2000 kg × (-25 m/s) = -50000 kg·m/s to the west
Total initial momentum = Momentum of Car A + Momentum of Car B
= 37500 kg·m/s to the east - 50000 kg·m/s to the west
Step 2: Calculate the final momentum.
After the collision, Car A goes off with a velocity of 10 m/s to the west. We need to calculate the velocity of Car B after the collision.
Let's assume the final velocity of Car B is v m/s to the west.
Final momentum of Car B = Mass of Car B × Final velocity of Car B
= 2000 kg × (-v) kg·m/s to the west
Since the two vehicles are not sticking together after the collision, the total final momentum will be the sum of the final momentum of Car A and the final momentum of Car B.
Total final momentum = Mass of Car A × Final velocity of Car A + Mass of Car B × Final velocity of Car B
Step 3: Apply the conservation of momentum principle.
According to the principle of conservation of momentum, the total initial momentum is equal to the total final momentum.
Total initial momentum = Total final momentum
(37500 kg·m/s to the east) + (-50000 kg·m/s to the west) = (Mass of Car A × Final velocity of Car A) + (Mass of Car B × Final velocity of Car B)
Now we can substitute the given values and solve for the final velocity of Car B.