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 -15 m/s (assuming the missing part is -15 m/s for consistency). they undergo an inelastic collision. what is the total combined momentum of both the carts before the collision?
$m_1\vec{v}_1 + m_2\vec{v}_2 = (m_1 + m_2)\vec{v}$
$vec{p} = mvec{v}$
options:
-13 kg·m/s
8.00 kg·m/s
7.0 kg·m/s
5.0 kg·m/s
4.0 kg·m/s
3.0 kg·m/s

Explanation:

Step1: Identify given values

Red cart: $m_1=2.0\ \text{kg}$, $v_1=4.0\ \text{m/s}$; Blue cart: $m_2=1.0\ \text{kg}$, $v_2=-5.0\ \text{m/s}$ (left direction is negative)

Step2: Calculate momentum of red cart

$p_1 = m_1v_1 = 2.0 \times 4.0 = 8.0\ \text{kg·m/s}$

Step3: Calculate momentum of blue cart

$p_2 = m_2v_2 = 1.0 \times (-5.0) = -5.0\ \text{kg·m/s}$

Step4: Sum momenta for total momentum

$p_{\text{total}} = p_1 + p_2 = 8.0 + (-5.0)$

Answer:

3.0 kg·m/s