Question

In a collision, a 15 kg object moving with a velocity of 3 m/s transfers some of its momentum to a 5 kg object. What would be the velocity of the 5 kg object after the collision if the 15 kg object is still moving at 1 m/s?

Answer 1

The key to solve this problem is the conservation of momentum. The momentum of an object is defined as the product between the mass and the velocity, and it's usually labelled with the letter $p$:

$p=mv$

The total momentum is the sum of the momentums. The initial situation is the following:

$m_A=15,\quad v_A=3,\quad m_B=5,\quad v_B=0$

(it's not written explicitly, but I assume that the 5-kg object is still at the beginning).

So, at the beginning, the total momentum is

$p=m_Av_A+m_Bv_B=15\cdot 3+5\cdot 0=45$

At the end, we have

$m_A=15,\quad v_A=1,\quad m_B=5,\quad v_B=x$

(the mass obviously don't change, the new velocity of the 15-kg object is 1, and the velocity of the 5-kg object is unkown)

After the impact, the total momentum is

$p=m_Av_A+m_Bv_B=15\cdot 1+5\cdot x=15+5x$

Since the momentum is preserved, the initial and final momentum must be the same. Set an equation between the initial and final momentum and solve it for $x$, and you'll have the final velocity of the 5-kg object.