- #1

I_Try_Math

- 59

- 15

- Homework Statement
- Three 70-kg deer are standing on a flat 200-kg rock that is on an ice-covered pond. A gunshot goes off and the deer scatter, with deer A running at ##(15\hat{i} + 5\hat{j})\frac{m}{s}##, deer B running at ##(-12\hat{i} + 8\hat{j})\frac{m}{s}##, and deer C running at ##(1.2\hat{i} - 18\hat{j})\frac{m}{s}##. What is the velocity of the rock on which they were standing?

- Relevant Equations
- ##\rho_i=\rho_f##

##\vec{\rho_{D1,i}}+\vec{\rho_{D2,i}}+\vec{\rho_{D3,i}}+\vec{\rho_{R,i}} = \vec{\rho_{D1,f}} +\vec{\rho_{D2,f}} +\vec{\rho_{D3,f}} +\vec{\rho_{R,f}}##

##\vec{0} = \vec{\rho_{D1,f}} +\vec{\rho_{D2,f}} +\vec{\rho_{D3,f}} +\vec{\rho_{R,f}}##

##\vec{0} = m_D(15\hat{i} + 5\hat{j}) + m_D(-12\hat{i} + 8\hat{j}) + m_D(1.2\hat{i} - 18\hat{j}) + m_R\vec{v_{f,R}} ##

##\vec{0} = m_D((15\hat{i} + 5\hat{j}) + (-12\hat{i} + 8\hat{j}) + (1.2\hat{i} - 18\hat{j})) + m_R\vec{v_{f,R}}##

##\vec{0} = m_D(4.2\hat{i}-5\hat{j}) + m_R\vec{v_{f,R}}##

##\vec{0} = (294\hat{i}-350\hat{j}) + 200\vec{v_{f,R}}##

##(-294\hat{i}+350\hat{j}) = 200\vec{v_{f,R}}##

##\vec{v_{f,R}} = (-1.47\hat{i}+1.75\hat{j})\frac{m}{s}##

Textbook says the correct answer is ## (-0.21\hat{i} + 0.25\hat{j})\frac{m}{s}##. Are my assumptions with respect to how conservation of momentum works in this case wrong? Any help is appreciated.

##\vec{0} = \vec{\rho_{D1,f}} +\vec{\rho_{D2,f}} +\vec{\rho_{D3,f}} +\vec{\rho_{R,f}}##

##\vec{0} = m_D(15\hat{i} + 5\hat{j}) + m_D(-12\hat{i} + 8\hat{j}) + m_D(1.2\hat{i} - 18\hat{j}) + m_R\vec{v_{f,R}} ##

##\vec{0} = m_D((15\hat{i} + 5\hat{j}) + (-12\hat{i} + 8\hat{j}) + (1.2\hat{i} - 18\hat{j})) + m_R\vec{v_{f,R}}##

##\vec{0} = m_D(4.2\hat{i}-5\hat{j}) + m_R\vec{v_{f,R}}##

##\vec{0} = (294\hat{i}-350\hat{j}) + 200\vec{v_{f,R}}##

##(-294\hat{i}+350\hat{j}) = 200\vec{v_{f,R}}##

##\vec{v_{f,R}} = (-1.47\hat{i}+1.75\hat{j})\frac{m}{s}##

Textbook says the correct answer is ## (-0.21\hat{i} + 0.25\hat{j})\frac{m}{s}##. Are my assumptions with respect to how conservation of momentum works in this case wrong? Any help is appreciated.