Question

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

Answer 1

22.4 m/s

Step-by-step explanation:

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:

`p_b=p_a\\\\`

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

`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`

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

`p_a=p_b=0\\\\-v_c=(m_Zv_Z+m_Jv_J)/(m_c)\\\\-v_c=((70kg)(4m/s)+(45kg)(4m/s))/(15kg)=-22.4(m)/(s)`

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