A running man has half the kinetic energy than a boy of half his mass has. The man speeds up by I $$m/$$$$sec$$ and then has the same kinetic energy as the boy. What were the original speeds of man and boy respectively?

Question

Infinity Learn · Accepted Answer

Let, M $$=$$ mass of man, m $$=$$ mass of boyV $$=$$ speed of man, v $$=$$ speed of boyGiven: $$12MV2$$ $$=$$ $$12(12mv2)$$, As m $$=$$ $$M2So$$ $$12MV2$$ $$=$$ $$12(12$$×$$M2v2)$$, Hence, $$v2$$ $$=$$ $$4V2$$ or v $$=2$$ VWhen the man speeds up by I m.$$/s$$, then we $$get12M(V+1)2$$ $$=$$ $$12mv2$$ $$=$$ $$12M2(4V2)or$$ $$(V+1)2$$ $$=$$ $$2V2$$ or $$V2-2V-1$$ $$=$$ $$0Solving$$ we get: V:$$2.4$$ $$m/s$$ and v : $$4.8$$ $$m/s$$

A running man has half the kinetic energy than a boy of half his mass has. The man speeds up by I m/sec and then has the same kinetic energy as the boy. What were the original speeds of man and boy respectively?

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