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  4. When a man increases his speed by 2 m/s, he finds that his kinetic energy is doubled, the original speed of the man is:

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Q. When a man increases his speed by 2 m/s, he finds that his kinetic energy is doubled, the & original speed of the man is:

MGIMS WardhaMGIMS Wardha 2006

Solution:

$ KE=K=\frac{1}{2}m{{v}^{2}} $ Given: $ {{v}_{2}}={{v}_{1}}+2 $ $ \therefore $ $ \frac{{{K}_{1}}}{{{K}_{2}}}={{\left( \frac{{{v}_{1}}}{{{v}_{2}}} \right)}^{2}} $ Or $ \frac{{{K}_{1}}}{{{K}_{2}}}={{\left( \frac{{{v}_{1}}}{{{v}_{2}}} \right)}^{2}} $ Or $ \frac{{{K}_{1}}}{2{{K}_{2}}}=\frac{v_{1}^{2}}{{{({{v}_{1}}+2)}^{2}}} $ Or $ v_{1}^{2}+4{{v}_{1}}+4=2v_{1}^{2} $ Or $ v_{1}^{2}-4{{v}_{1}}-4=0 $ $ {{v}_{1}}=\frac{4\pm \sqrt{16+6}}{2} $ $ =\frac{4\pm \sqrt{32}}{2} $ $ =2(\sqrt{2}+1)m/s $