A body is projected with kinetic energy 100J at an angle 45° with horizontal. What fraction of kinetic energy will be the potential energy at the highest point? from Physics Motion in A Plane Class 11 Manipur Board
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Physics Part I

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A body is projected with kinetic energy 100J at an angle 45° with horizontal. What fraction of kinetic energy will be the potential energy at the highest point?

If a body is projected with kinetic energy K at angle θ, then kinetic energy at highest point is K cos2θ.

Therefore, potential energy of the body at highest point is,

P.E. = space space straight K minus straight K space c o s squared straight theta space equals space straight K left parenthesis 1 minus c o s squared straight theta right parenthesis space
space space space space space space space space space space space space space space space space space space space space space space space space equals space straight K space s i n squared straight theta 

Fractional potential energy at highest point is, 

space space space fraction numerator Potential space Energy over denominator Total space energy space at space the space time space of space projection end fraction

  
equals fraction numerator straight K space sin squared straight theta over denominator straight K end fraction equals sin squared straight theta           

Here, we have

K = 100 J and straight theta space equals space 45 to the power of straight o   
Fractional potential energy at highest point is, 

                      space space space sin squared 45 degree space equals space 0.5

At the highest point, K.E will be 0.5 times the P.E at the highest point. 
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