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 0.57 m/s 0.57 m/s 1.14 m/s 1.14 m/s 1.10 m/s 1.10 m/s 0.55 m/s
To solve this problem, we can apply the principle of conservation of momentum.
The momentum before the collision is equal to the momentum after the collision.
Momentum (p) is calculated by multiplying mass (m) by velocity (v):
p = m * v
For the first car with a mass of 1,250 kg and velocity of 2.24 m/s:
p1 = 1,250 kg * 2.24 m/s = 2,800 kg*m/s
For the second car with a mass of 1,300 kg and velocity initially at rest (0 m/s):
p2 = 1,300 kg * 0 m/s = 0 kg*m/s
After the collision, the cars stick together and move forward as one body. Let's call their final velocity v_f. Since they move together, their combined mass is the sum of their individual masses: 1,250 kg + 1,300 kg = 2,550 kg.
Therefore, the momentum after the collision is:
p_f = 2,550 kg * v_f
Since momentum is conserved, p_f must be equal to the initial momentum (p1 + p2):
p_f = p1 + p2
Thus, 2,550 kg * v_f = 2,800 kg*m/s + 0 kg*m/s
2,550 kg * v_f = 2,800 kg*m/s
Solving for v_f:
v_f = (2,800 kg*m/s) / 2,550 kg
v_f ≈ 1.1 m/s
Therefore, the two cars will move forward together at a speed of approximately 1.10 m/s.