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 1.10 m/s 1.10 m/s 1.14 m/s 1.14 m/s 0.55 m/s 0.55 m/s
To solve this problem, we can use the principles of conservation of momentum.
The momentum before the collision can be calculated using the formula:
Momentum before the collision = mass of car 1 * velocity of car 1 + mass of car 2 * velocity of car 2
= (1250 kg)(2.24 m/s) + (1300 kg)(0 m/s)
= 2800 kg·m/s
Since the two cars stick together and move forward after the collision, their combined mass is the sum of their individual masses:
Combined mass = mass of car 1 + mass of car 2
= 1250 kg + 1300 kg
= 2550 kg
To find the final velocity of both cars, we can divide the momentum before the collision by the combined mass:
Final velocity = Momentum before collision / Combined mass
= 2800 kg·m/s / 2550 kg
≈ 1.10 m/s
Therefore, the two cars will move forward with a velocity of approximately 1.10 m/s.