A) \[10\text{ m }{{\text{s}}^{-1}}\]
B) \[20\text{ m }{{\text{s}}^{-1}}\]
C) \[30\text{ m }{{\text{s}}^{-1}}\]
D) \[40\text{ m }{{\text{s}}^{-1}}\]
Correct Answer: B
Solution :
Change in gravitational potential energy of the skier \[{{E}_{P}}=mgh=50\times 10\times [60-20]\] \[=20000J=2\times {{10}^{4}}J\] Kinetic energy, \[{{E}_{K}}=50%\] of \[{{E}_{P}}=\frac{1}{2}\times 2\times {{10}^{4}}J=1\times {{10}^{4}}J\] \[{{E}_{K}}=\frac{1}{2}m{{v}^{2}}\Rightarrow v=\sqrt{\frac{2{{E}_{K}}}{m}}=\sqrt{\frac{2\times 1\times {{10}^{4}}}{50}}=20m{{s}^{-1}}\]
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