sayid made a chart listing data of two colliding objects.\ncollision: two objects stick together\n|object|mas…

sayid made a chart listing data of two colliding objects.\ncollision: two objects stick together\n|object|mass before collision (kg)|velocity before collision (m/s)|mass after collision (kg)|velocity after collision (m/s)|\n|----|----|----|----|----|\n|x|300|10|400|?|\n|y|100|-6|\naccording to the law of conservation of momentum, what is the missing value in the chart?\n4\n6\n10\n16

Answer

Explanation:

Step1: Recall momentum - conservation formula

The law of conservation of momentum is $m_1u_1 + m_2u_2=(m_1 + m_2)v$, where $m_1$ and $m_2$ are the masses before collision, $u_1$ and $u_2$ are the velocities before collision, and $(m_1 + m_2)$ is the mass after collision and $v$ is the velocity after collision.

Step2: Identify values from the table

For object X, $m_1 = 300$ kg, $u_1=10$ m/s. For object Y, $m_2 = 100$ kg, $u_2=-6$ m/s. The combined mass after collision $m_1 + m_2=400$ kg.

Step3: Substitute values into the formula

$300\times10+100\times(- 6)=(300 + 100)v$. First, calculate the left - hand side: $300\times10+100\times(-6)=3000-600 = 2400$. The right - hand side is $400v$.

Step4: Solve for $v$

We have the equation $2400 = 400v$. Divide both sides by 400: $v=\frac{2400}{400}=6$ m/s.