Question

the red cart has a mass of 2.0 kg and an initial velocity of 4.0 m/s. the blue cart has a mass of 1.0 kg and an initial velocity of -5.00 m/s. the carts collide in an inelastic collision. what is the velocity of both carts after the collision?
$m_1\vec{v}_1 + m_2\vec{v}_2 = (m_1 + m_2)\vec{v}$
$\vec{p} = m\vec{v}$
-13 m/s
-8.0 m/s
-7.0 m/s
-5.00 m/s
-4.0 m/s

Explanation:

Step1: List given values

$m_1=2.0\ \text{kg}$, $v_1=4.0\ \text{m/s}$, $m_2=1.0\ \text{kg}$, $v_2=-5.00\ \text{m/s}$

Step2: Rearrange for final velocity

$\bar{v}=\frac{m_1\bar{v}_1 + m_2\bar{v}_2}{m_1+m_2}$

Step3: Substitute values into formula

$\bar{v}=\frac{(2.0\times4.0)+(1.0\times(-5.00))}{2.0+1.0}=\frac{8.0-5.00}{3.0}=\frac{3.0}{3.0}$

Answer:

1.0 m/s
(Note: This correct result does not match the provided options, indicating a potential error in the listed choices. The calculation follows the conservation of momentum for perfectly inelastic collisions.)