Can you help me understand this question in detail with step-by-step methods and

Question

Can you help me understand this question in detail with step-by-step methods and, the formula that is being used so that, I can understand better.

A 2.0-kg cart moving to the right with a speed of 6.0 m/s has a head-on collision with a 5.0-kg cart that is initially moving to the left with a speed of 2.0 m/s. After the collision, the 2.0-kg cart is moving to the left with a speed of 3.0 m/s. What is the final velocity of the 5.0-kg cart?

(a) 0.80 m/s to the left (c) zero m/s (e) 1.2 m/s to the left (b) 0.80 m/s to the right (d) 1.2 m/s to the right

Explanation / Answer

Using momentum conservation:

Pi = Pf

m1u1 + m2u2 = m1v1 + m2v2

right side is +ve and left side is -ve

u1 = +6 m/sec

u2 = -2 m/sec

v1 = -3 m/sec

So,

2*6 - 5*2 = -2*3 + 5*v2

v2 = 8/5 = +1.6 m/sec

+ve sign means towards the right

Correct answer should be +1.6 m/sec to the right, which is not given in any option.

Please check the question again and let me know if there is a mistake in any given value.

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