Question

1. in a physics lab, a 1.0 kg cart (cart a) moving rightward at 2.0 m/s collides head - on with a 1.0 kg cart (cart b) moving leftward at 1.0 m/s. after the collision, the two carts stick together and move as a single object. determine the post - collision velocity (include the direction!) of the combined carts. (1 point) select your answer

Explanation:

Step1: Define variables and apply conservation of momentum

Let the right - ward direction be positive. $m_1 = m_2=1.0\ kg$, $v_1 = 2.0\ m/s$, $v_2=- 1.0\ m/s$. According to the law of conservation of momentum $m_1v_1 + m_2v_2=(m_1 + m_2)v$.

Step2: Substitute values into the formula

$(1.0\times2.0)+(1.0\times(-1.0))=(1.0 + 1.0)v$.
First, calculate the left - hand side: $2.0-1.0 = 1.0\ kg\cdot m/s$. The right - hand side is $2.0v$.

Step3: Solve for $v$

We have the equation $1.0=2.0v$. Then $v=\frac{1.0}{2.0}=0.5\ m/s$.

Answer:

The post - collision velocity is $0.5\ m/s$ to the right.