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$10.(30$ pts$)$ A large block with mass $m_1=50kg$ is on a frictionless horizontal surface. Another smaller block with mass $m_2=20kg$ is placed on top of the first block as shown. The coefficients of friction between the two blocks are ${}_s=0\mathrm{.}60$ and ${}_k=0\mathrm{.}30.$ A force $P=200N$ is applied to the top block at an angle $=30$ below the horizontal as shown. Find the acceleration of each block. $($Hint: First determine whether or not the top block slides relative to the bottom block$).$