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 elastic collision. after the collision the red cart has a velocity of -2.0 m/s. what is the velocity of the blue cart after the collision?
$m_1v_1 + m_2v_2 = m_1v_1 + m_2v_2$
$p = mv$
-13 m/s
-8.0 m/s
7.0 m/s
5.0 m/s
4.0 m/s
3.0 m/s

Explanation:

Step1: List given values

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

Step2: Rearrange momentum formula for $v_2'$

$v_2' = \frac{m_1v_1 + m_2v_2 - m_1v_1'}{m_2}$

Step3: Substitute values into formula

$v_2' = \frac{(2.0\times4.0) + (1.0\times-5.00) - (2.0\times-2.0)}{1.0}$

Step4: Calculate step-by-step

First compute each term:
$2.0\times4.0=8.0$, $1.0\times-5.00=-5.0$, $2.0\times-2.0=-4.0$
Then:
$v_2' = \frac{8.0 - 5.0 - (-4.0)}{1.0} = \frac{8.0 - 5.0 + 4.0}{1.0} = 7.0\ \text{m/s}$

Answer:

7.0 m/s