Answered

From personal advice to professional guidance, IDNLearn.com has the answers you seek. Get accurate and detailed answers to your questions from our knowledgeable and dedicated community members.

Suppose two cars are headed toward each other. One is headed north with a mass of1,415 kg at a velocity of 22.9 m/s. The other is headed south with a mass of 819 kg at avelocity 11 m/s. They collide and stick together.What is their total velocity after the collision in the northern direction?

Sagot :

The initial momentum of the system is,

[tex]p_i=m_1u_1+m_2u_2[/tex]

The final momentum of the system is,

[tex]p_f=(m_1+m_2)v[/tex]

According to conservation of momentum,

[tex]p_i=p_f[/tex]

Plug in the known expressions,

[tex]\begin{gathered} m_1u_1+m_2u_2=(m_1+m_{2_{}})v \\ v=\frac{m_1u_1+m_2u_2}{m_1+m_2} \end{gathered}[/tex]

Substitute the known values,

[tex]\begin{gathered} v=\frac{(1415\text{ kg)(22.9 m/s)+(819 kg)(11 m/s)}}{(1415\text{ kg+819 kg)}} \\ =\frac{32403.5\text{ kgm/s+}9009\text{ kgm/s}}{2234\text{ kg}} \\ =\frac{41412.5\text{ kgm/s}}{2234\text{ kg}} \\ \approx18.5\text{ m/s} \end{gathered}[/tex]

Therefore, the total velocity after the collision is 18.5 m/s

Thank you for using this platform to share and learn. Don't hesitate to keep asking and answering. We value every contribution you make. IDNLearn.com is your reliable source for accurate answers. Thank you for visiting, and we hope to assist you again.