Question

Aight here's the question:

Answer 1

Answer:

$5.12\:\text{m/s}$

Explanation:

From the conservation of momentum, the total momentum of the system before and after the collision must be the same. Therefore, let the momentum of Homeboy Joe be $p_b$ and let the mass of Homegirl Jill be $p_j$. We can write the following equation:

$p_{bi}+p_{ji}=p_{bf}+p_{jf}$, where subscripts $i$ and $f$ represent initial and final momentum respectively.

The momentum of an object is given by $p=mv$.

Therefore, we have:

$m_{b}v_{bi}+m_{j}v_{ji}=m_{b}v_{bf}+m_{b}v_{jf}$ (some messy subscripts but refer to the values being plugged in you're confused what corresponds with what).

Plugging in values, we have:

$99.5\cdot 6.65 + 68.8\cdot (-1.10)=99.5\cdot 2.35+ 68.8\cdot v_{jf}$.

Solving, we get:

$v_{jf}=\frac{99.5\cdot 6.65+68.8\cdot (-1.10)-99.5\cdot2.35}{68.8},\\v_{jf}=5.11875,\\v_{jf}\approx \boxed{5.12\:\text{m/s}}$.

It's important to note that velocity is vector quantity, so the negative velocity assigned to Jill simply implies she is moving at $1.10\:\text{m/s}$ in the opposite of Joe's direction. After the collision, she is now moving $5.12\:\text{m/s}$ in the same direction that Joe was initially moving, due to Joe's relatively large mass and initial velocity.