### Physics Problem: Elastic Collision#### Problem StatementTwo balls (which we will label as **ball 1** and **ball 2**) undergo a perfectly elastic head-on collision, with **ball 2** initially at rest. Suppose the incoming ball (**ball 1**) has a speed of 200 m/s. Assume all motion is one-dimensional and ignore friction and drag.#### Part (a)**Task**: Write out algebraic expressions for both the Law of Conservation of Momentum and the Law of Conservation of Energy as they apply to this isolated system. - For this part of the problem, write the expressions for the Conservation of Momentum and Conservation of Energy for this system and plug in any known zero values but do not plug in any other numbers.- Leave the masses of the balls (**m1** and **m2**) as algebraic variables.#### Part (b)**Task**: Compute the final speeds (**v1f** and **v2f**) and directions (± x-direction, since the motion is assumed to be 1-dimensional) of the balls.- We could use the conservation laws from part (a) to solve for these final speeds, but this would involve a lot of algebraic manipulation. Instead, the algebraic expressions for the final speeds are given by:\[ v_{1f} = \frac{m_1 - m_2}{m_1 + m_2} \cdot v_{10} \]\[ v_{2f} = \frac{2m_1}{m_1 + m_2} \cdot v_{10} \]- Suppose **m2** is much bigger than **m1** (**m2 >> m1**). What are the final speeds **v1f** and **v2f**, and their directions, if we take **m1** = 10 kg and **m2** = 10 (metric) tons = 10000 kg?#### Part (c)**Task**: Compute the final speeds **v1f** and **v2f** if we take **m1** = 0 kg and **m2** = 10 (metric) tons = 10000 kg. - Compare this to the results from part (b).#### Part (d)**Task**: Take your algebraic expressions for the conservation laws you wrote down in part (a) and plug in **m

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Two balls (which we will label ball 1 and ball 2) undergo a perfectly elastic head-on collision, with ball 2 initially at rest. Suppose the incoming ball (ball 1) has a speed of 200 m/s. Assume all motion is one-dimensional and ignore friction and drag. (a.) Write out algebraic expression for both the Law of Conservation of Momentum and the Law of Conservation of Energy as they apply for this isolated system. (That is, for this part of the problem I want you to write the Conservation of Momentum equation and the Conservation of Energy equation for this system and plug in any known zero values but do not plug in any other numbers.) For the moment, leave the masses of the balls (m1 and m2) as algebraic variables (as I am not giving you numerical values for the masses just yet). (b.) We want to compute the final speeds (vif and v2f) and directions (±x-direction, since the motion is assumed to be 1 dimensional) of the balls. We could use our conservation laws from part (a.) together to solve for these final speeds, but doing so will take a lot of algebraic manipulations. So, instead, I'll give you the algebraic expressions you would find for vif and v2f. They are found to be given by 2m1 mị – M2 V10 mị + m2 Vif V2f = -V10- mị + m2 Suppose m2 is much much bigger than m1 (m2 >> m1). What are the final speeds vif and v2f, and their directions, if we take m1 = 10 kg and m2 = 10 (metric) tons = 10000 kg? (c.) Compute the final speeds vif and v2f if we take m1 = 0 kg and m2 = 10 (metric) tons = 10000 kg? How does this compare to your results from part (b.)? (d.) Take your algebraic expressions for the conservation laws you wrote down in part (a.) and plug in mị = 0 kg but leave m2 as an unspecified value (that is, leave m2 as an algebraic variable). Now it should be much easier to do the algebra needed to obtain algebraic expressions for vif and v2f. Work out this algebra and show that you get the same result as you would by simply plugging m1 = 0 into the equations for vif and v2f that I gave you in part (b.). Note: If you find yourself struggling with the algebra, please reach out and ask for help! I'm glad to help with algebra, as that's not what I'm testing you on here.