Question

# A 2.002.3-kg cart is rolling across a frictionless, horizontal track toward a 0.601.5-kg cart that is...

A 2.002.3-kg cart is rolling across a frictionless, horizontal track toward a 0.601.5-kg cart that is held initially at rest. The carts are loaded with strong magnets that cause them to attract one another. Thus, the speed of each cart increases. At a certain instant before the carts collide, the first cart’s velocity is 4.80 14.5 m/s, and the second cart’s velocity is 1.9021.9 m/s. What was the velocity of the first cart when the second cart was still at rest?

Your given values in the questions look terrible...How can there be two decimals in one number.

Anyway, Let m1 be the mass of first cart and m2 be the mass of second cart. Let v1 be the velocity of first cart and v2 be the velocity of second cart.

Then total mometum is

m1*v1 + m2*v2 = Total momentum

Here notice one thing, due to attrcation, one cart moves in opposite direction. So total momentum becomes

Total momentum = m1*v1 - m2*v2

Just put the values and find total momentum

Now when second cart is at rest v2 = 0

then m1*v1 = total momentum

v1 = total momentum / m1

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