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
1.10 m/s
1.10 m/s
0.57 m/s
0.57 m/s
1.14 m/s
To solve this problem, we will use the principle of conservation of momentum.
The momentum before the collision is given by the equation:
Momentum = mass × velocity
Let's calculate the momentum of the first car:
Momentum(1st car) = mass(1st car) × velocity(1st car)
= 1250 kg × 2.24 m/s
= 2800 kg⋅m/s
The momentum of the second car is:
Momentum(2nd car) = mass(2nd car) × velocity(2nd car)
= 1300 kg × 0 m/s (since the second car is stopped)
= 0 kg⋅m/s
According to the conservation of momentum, the total momentum before the collision must be equal to the total momentum after the collision.
So, the total momentum after the collision is:
Total momentum = Momentum(1st car) before collision + Momentum(2nd car) before collision
= 2800 kg⋅m/s + 0 kg⋅m/s
= 2800 kg⋅m/s
Since the two cars stick together and move forward, their combined mass is the sum of their individual masses:
Total mass = mass(1st car) + mass(2nd car)
= 1250 kg + 1300 kg
= 2550 kg
To find the final velocity, we use the equation:
Final velocity = Total momentum / Total mass
= 2800 kg⋅m/s / 2550 kg
≈ 1.10 m/s
So, the correct answer is 1.10 m/s.