Answer:
[tex]V_H=-20.45m/s[/tex]
Explanation:
By kinematics:
[tex]V_R=V_o+a*t=0+(10m/s^2)*(2s)=20m/s[/tex]
The rocket's height at this point is:
[tex]V_R^2=V_o^2+2*a*H_R[/tex]
[tex]H_R=20m[/tex]
On the lighter fragment:
[tex]V_f^2=V_L^2-2*g*H_L[/tex] where Vf=0. Solving for VL:
[tex]V_L=\sqrt{2*g*H_L}=100.99m/s[/tex]
By conservation of the momentum:
[tex]3*m*V_R=2*m*V_H+m*V_L[/tex]
Solving for [tex]V_H[/tex]:
[tex]V_H=\frac{3*V_R-V_L}{2}=-20.45m/s[/tex]
