Q$1.$ Figure given below shows block A with $10$ kg and block $B$ with $5$ kg of masses, where both are placed on frictionless surfaces and start their $($sliding$)$ motion from rest on an inclined plane which makes an angle of $20$ with the horizontal surface. Determine $i)$ the absolute acceleration of block $A,a_{\frac{A}{G}}$ ii$)$ the absolute acceleration of block $B,a_{\frac{B}{G}}$ iii$)$ the relative acceleration of block $B$ with respect to block $A,a_{\frac{B}{A}}iv)$ The time, $t_{\text{f}\text{a}\text{l}\text{l}}$ when block $B$ falls over block $A($hint: note that block $B$ must cover $2m$ until it falls over block A$)$ v$)$ The velocities, $v_{\frac{A}{G}},v_{\frac{B}{G}},$ and $v_{\frac{B}{A}}$ when block $B$ falls down $vi)$ Use Principle of Work and Energy to show that $T_1+V_1=T_2+V_2,$ where $T_1$ and $V_1$ are energy kinetic and potential energy at $t=0,$ while $T_2$ and $V_2$ are energy kinetic and potential energy at $t_{\text{f}\text{a}\text{l}\text{l}}.(40$ points$)$