3. Jack and Zack are standing on a crate at rest on a frictionless horizontal surface. Jack has a mass of 70 kg, Zack has a mass of 45 kg, and the crate has a mass of 15 kg. In what follows, we will see that both jump of the crate. You may assume that they push themselves off with a speed of 4 m/s relative to the crate and in a direction that is essentially horizontal.a) what is the final speed of the crate if Jack and Zack jump simultaneously, in the same direction

To find the speed of the crate you take into account the momentum conservation. The momentum before Jack and Zack jump must be equal to the momentum after. Then you have:

[tex]p_b=p_a\\\\[/tex]

Furthermore, you take into account that the momentum before, when crater, Jack and Zack are at rest, the momentum is zero. Hence:

[tex]p_b=(m_Z+m_J+m_c)v=0\\\\m_Z=45kg\\\\m_J=70kg\\\\m_c=15kg\\\\p_a=m_Zv_Z+m_Jv_J+m_cv_c[/tex]

but you know what are the velocities of Zack and Jack after they jump.

[tex]p_a=p_b=0\\\\-v_c=\frac{m_Zv_Z+m_Jv_J}{m_c}\\\\-v_c=\frac{(70kg)(4m/s)+(45kg)(4m/s)}{15kg}=-22.4\frac{m}{s}[/tex]

the minus sign means that the velocity of the crater is in an opposite direction of the spee of Jack and Zack.

hence, the speed of the crater is 22/4m/s