Answer:
1.53 m/s
Explanation:
Given:
Mass of the car (M) = 1300 kg
Mass of the coal (m) = 400 kg
Initial velocity of the car (U) = 2 m/s
Initial velocity of the coal (u) = 0 m/s (Since it is dropped)
When the coal is dropped into the car, then they move with same final velocity.
Let the final velocity be 'v' m/s.
For a closed system, the law of conservation of momentum holds true.
So, initial momentum is equal to final momentum of the car-coal system.
Initial momentum of the car = ![MU=1300\times 2=2600\ Ns](https://tex.z-dn.net/?f=MU%3D1300%5Ctimes%202%3D2600%5C%20Ns)
Initial momentum of the coal = ![mu=0\ Ns](https://tex.z-dn.net/?f=mu%3D0%5C%20Ns)
Total initial momentum is the sum of the above two momentums.
So, total initial momentum = 2600 + 0 = 2600 Ns
Now, final momentum is given as the product of combined mass and final velocity. So,
Final momentum of the system = ![(M+m)v=(1300+400)v=1700v](https://tex.z-dn.net/?f=%28M%2Bm%29v%3D%281300%2B400%29v%3D1700v)
Now, from law of conservation of momentum,
Initial momentum = Final momentum
![2600=1700v\\\\v=\frac{2600}{1700}\\\\v=1.53\ m/s](https://tex.z-dn.net/?f=2600%3D1700v%5C%5C%5C%5Cv%3D%5Cfrac%7B2600%7D%7B1700%7D%5C%5C%5C%5Cv%3D1.53%5C%20m%2Fs)
Therefore, the final velocity of either of the two masses is same is equal to 1.53 m/s.