Answer:
[tex]x_{L} = 106\,m[/tex]
Explanation:
Each piece is analyzed by using the Principle of Momentum Conservation and the Impulse Theorem:
Heavier object:
[tex](2\cdot M)\cdot (0) + F\cdot \Delta t = (2\cdot M)\cdot v_{H}[/tex]
Lighter object:
[tex]M\cdot (0) + F\cdot \Delta t = M\cdot v_{L}[/tex]
After the some algebraic handling, the following relationship is found:
[tex]M\cdot v_{L} = 2\cdot M\cdot v_{H}[/tex]
[tex]v_{L} = 2\cdot v_{H}[/tex]
Given that both pieces have horizontal velocities only and both are modelled as projectiles, the horizontal component of velocity remains constant and directly proportional to travelled distance. Then:
[tex]\frac{v_{L}}{v_{H}} = \frac{x_{L}}{53\,m}[/tex]
[tex]2 = \frac{x_{L}}{53\,m}[/tex]
[tex]x_{L} = 106\,m[/tex]
