Answer:
The body flies off to the left at 9.1 m/s
Explanation:
Law Of Conservation Of Linear Momentum
It states the total momentum of a system of bodies is conserved unless an external force is applied to it. The formula for the momentum of a body with mass m and speed v is
P=mv.
If we have a system of bodies, then the total momentum is the sum of the individual momentums:
[tex]P=m_1v_1+m_2v_2+...+m_nv_n[/tex]
If a collision occurs and the velocities change to v', the final momentum is:
[tex]P'=m_1v'_1+m_2v'_2+...+m_nv'_n[/tex]
Since the total momentum is conserved, then:
P = P'
In a system of two masses, the equation simplifies to:
[tex]m_1v_1+m_2v_2=m_1v'_1+m_2v'_2\qquad\qquad[1][/tex]
Wall-E robot is initially at rest, its two parts together. His head has a mass of m1=0.75 kg and his body has a mass of m2=6.2 kg. Both parts have initial speeds of zero v1=v2=0.
After the explosion, his head flies off to the right at v1'=75 m/s. We are required to find the speed of his body v2'. Solving [1] for v2':
[tex]\displaystyle v'_2=\frac{m_1v_1+m_2v_2-m_1v'_1}{m_2}[/tex]
Substituting values:
[tex]\displaystyle v'_2=\frac{0.75*0+6.2*0-0.75*75}{6.2}[/tex]
[tex]\displaystyle v'_2=-9.1 \ m/s[/tex]
The body flies off to the left at 9.1 m/s
