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 -5.0 m/s. the carts collide in an inelastic collision. what is the total combined momentum of both the 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 kg·m/s
-8.00 kg·m/s
-7.0 kg·m/s
-6.0 kg·m/s
-4.0 kg·m/s

Explanation:

Step1: Recall momentum conservation law

Total momentum before = total momentum after.

Step2: Calculate initial momentum of red cart

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

Step3: Calculate initial momentum of blue cart

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

Step4: Sum initial momenta for total final momentum

$p_{\text{total}} = p_1 + p_2 = 8.0 + (-5.0) = 3.0\ \text{kg·m/s}$
(Note: Based on the calculation, the correct answer is 3.0 kg·m/s, which does not match the listed options. Assuming a typo in the options, the closest intended correct value aligns with the calculation.)

Answer:

3.0 kg·m/s
(Note: None of the provided options match the calculated result. The correct total combined momentum after the collision is 3.0 kg·m/s.)