A car with a mass of 1,250 kg travels at 2.24 m/s and bumps into a stopped car with a mass of 1,300 kg. After the collision, the two cars stick together and move forward. How fast will they both move forward? Round your answer to two decimal places.(1 point)
Responses
0.55 m/s
0.55 m/s
1.14 m/s
1.14 m/s
1.10 m/s
1.10 m/s
0.57 m/s
To solve this problem, we can use the principle of conservation of momentum.
The momentum of an object is given by the product of its mass and velocity. The total momentum before the collision is equal to the total momentum after the collision.
Let's denote the velocity of the car after the collision as v.
The momentum before the collision can be calculated as the product of the mass and velocity of the first car:
Momentum of first car before collision = (mass of first car) * (velocity of first car)
= 1,250 kg * 2.24 m/s
The momentum of the second car before the collision is zero since it is stopped.
Let's assume that the total velocity of the two cars after the collision is v.
The momentum after the collision is equal to the sum of the momentum of the first car and the momentum of the second car:
Momentum after collision = (total mass) * (total velocity)
The total mass is the sum of the masses of the two cars:
Total mass = mass of the first car + mass of the second car
= 1,250 kg + 1,300 kg
Since the two cars stick together and move forward, their total momentum after the collision is:
Momentum after collision = (total mass) * (total velocity)
= (1,250 kg + 1,300 kg) * v
Setting the momentum before the collision equal to the momentum after the collision, we have:
1,250 kg * 2.24 m/s = (1,250 kg + 1,300 kg) * v
Simplifying this equation, we get:
2,800 kg * m/s = 2,550 kg * v
Dividing both sides of the equation by 2,550 kg, we find:
m/s = v
Rounding this value to two decimal places, the velocity of the combined cars after the collision is:
0.57 m/s
Therefore, the correct answer is 0.57 m/s.