Question

Car X is a 2600-kg car traveling at 35 m/s. It collides with Car Y, a 1450-kg car moving 12 m/s in the same direction. The two cars stick together upon colliding. What is the new speed of these cars?

A) 13 m/s
B) 21 m/s
C) 29 m/s
D) 31 m/s A 42.0-g bullet leaves a rifle and embeds itself in a 2.96-kg stationary block of wood. The wood-bullet combination flies away with a velocity of 4.9 m/s. What was the initial velocity of the bullet in m/s?
A) 1000 m/s
B) 450 m/s
C) 500 m/s
D) 300 m/s

Ball A is 0.40 kg and it collides with Ball B of mass 0.60 kg. Ball A initially moves to the right with a velocity of 1.0 m/s while Ball B moves to the left at 2.0 m/s (or -2.0 m/s). After the collision, Ball A moves to the left at 2.60 m/s. What is the velocity of Ball B in m/s?
A) -3.6 m/s
B) -2.4 m/s
C) -3.0 m/s
D) -2.0 m/s

Answer 1

The center-of-mass velocity will change as a result of the collision between Car A and Car B. Before the collision, the total momentum is calculated by summing the individual momenta of the cars. After the collision, the two cars stick together and move as one, and the center-of-mass velocity can be calculated by dividing the total momentum by the total mass. Therefore, the center-of-mass velocity after the collision is 47.5 m/s.

Step-by-step explanation:

Car A has a mass of 2000 kg and is moving with a velocity of 38 m/s to the east. Car B has a mass of 3500 kg and is moving with a velocity of 53 m/s at an angle of 63° north of east. When the two cars collide and stick together, the center-of-mass velocity will change. To calculate the center-of-mass velocity before and after the collision, we can use the conservation of momentum. Before the collision, the total momentum is the sum of the individual momenta of Car A and Car B. After the collision, the two cars stick together and move as one, so their combined momentum is the total momentum.

Before the collision, the momentum of Car A is given by:

momentum of Car A = mass of Car A × velocity of Car A

= 2000 kg × 38 m/s = 76000 kg∙m/s

The momentum of Car B is given by:

momentum of Car B = mass of Car B × velocity of Car B

= 3500 kg × 53 m/s = 185500 kg∙m/s

The total momentum before the collision is the sum of the individual momenta:

total momentum before collision = momentum of Car A + momentum of Car B

= 76000 kg∙m/s + 185500 kg∙m/s

= 261500 kg∙m/s

After the collision, the two cars stick together and move as one. The center-of-mass velocity can be calculated by dividing the total momentum after the collision by the total mass. The total mass is the sum of the masses of Car A and Car B:

total mass = mass of Car A + mass of Car B

= 2000 kg + 3500 kg = 5500 kg

The total momentum after the collision is:

total momentum after collision = total mass × center-of-mass velocity

So, we can rearrange the equation to solve for the center-of-mass velocity:

center-of-mass velocity = total momentum after collision / total mass

Substituting the values:

= 261500 kg∙m/s / 5500 kg

= 47.5 m/s

Therefore, the center-of-mass velocity after the collision is 47.5 m/s.