Question

A box of 20kg has fall from 40m hight.
Question : In which point from that hight the potential energy will get equal of one-third of the kinetic energy? ​

Answer 1

GiveN :-

• A box has a mass of 20kg .
• It is falled from height of 40m .

To FinD :-

• The point at which the Kinetic energy is equal to the three times the Potential Energy.

AnsweR :-

Let us take that the point is x m from the top of the tower . So its height from down will be (40-x) . So now we are required to find the point at which the Potential Energy is one third of the Kinetic Energy. So ,

☯️ $\underline{\underline{\boldsymbol{ According\ to \ the \ Question :- }}}$

$\sf:\implies \pink{ \dfrac{1}{3}( Kinetic \ Energy)= Potential\ Energy} \\\\\sf:\implies \dfrac{1}{3}\bigg( \dfrac{1}{2}\times m \times v^2\bigg)= mgh \\\\\sf:\implies \dfrac{v^2}{6}= gh \\\\\sf:\implies \dfrac{(\sqrt{2gh})^2}{6}= 10(40-x)\\\\\sf:\implies \dfrac{2\times x}{6}=40-x \\\\\sf:\implies \dfrac{x}{3}=40 - x \\\\\sf:\implies x = 3(40-x)\\\\\sf:\implies x = 120 -3x\\\\\sf:\implies 3x + x =120 \\\\\sf:\implies 4x =120 \\\\\sf:\implies x =\dfrac{120}{4}\\\\\sf:\implies \boxed{\pink{\frak{ x = 30 \ meters }}}$

$\underline{\blue{\textsf{ Hence the required point is \textbf{30 m from above and 10m from down }.}}}$