STATEMENT-1-The-graph-between-kinetic-energy-and-vertical-displacement-is-a-straight-line-for-a-projectile-STATEMENT-2-The-graph-between-kinetic-energy-and-horizontal-displacement-is-a-straight-l

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Question Number 19476 by Tinkutara last updated on 11/Aug/17

$$\mathrm{STATEMENT}-1:\mathrm{The}\mathrm{graph}\mathrm{between}$$$$\mathrm{kinetic}\mathrm{energy}\mathrm{and}\mathrm{vertical}\mathrm{displacement}$$$$\mathrm{is}\mathrm{a}\mathrm{straight}\mathrm{line}\mathrm{for}\mathrm{a}\mathrm{projectile}.$$$$\mathrm{STATEMENT}-2:\mathrm{The}\mathrm{graph}\mathrm{between}$$$$\mathrm{kinetic}\mathrm{energy}\mathrm{and}\mathrm{horizontal}$$$$\mathrm{displacement}\mathrm{is}\mathrm{a}\mathrm{straight}\mathrm{line}\mathrm{for}\mathrm{a}$$$$\mathrm{projectile}.$$$$\mathrm{STATEMENT}-3:\mathrm{The}\mathrm{graph}\mathrm{between}$$$$\mathrm{kinetic}\mathrm{energy}\mathrm{and}\mathrm{time}\mathrm{is}\mathrm{a}\mathrm{parabola}$$$$\mathrm{for}\mathrm{a}\mathrm{projectile}.$$

Answered by ajfour last updated on 12/Aug/17

$$\mathrm{K}=\frac{1}{2}{\mathrm{mv}}^2=\frac{1}{2}\mathrm{m}({\mathrm{v}}_{\mathrm{y}}^2+{\mathrm{v}}_{\mathrm{x}}^2)$$$$=\frac{1}{2}\mathrm{m}[{\mathrm{v}}_{\mathrm{y}0}^2-2\mathrm{gy}+{\mathrm{v}}_{\mathrm{x}0}^2]$$$$\Rightarrow \mathrm{K}-\mathrm{y}\mathrm{graph}\mathrm{is}\mathrm{straight}\mathrm{line}$$$$\mathrm{further},\mathrm{since}\mathrm{y}=\mathrm{x}\left(\frac{{\mathrm{v}}_{\mathrm{y}0}}{{\mathrm{v}}_{\mathrm{x}0}}\right)-\frac{{\mathrm{gx}}^2}{{2\mathrm{u}}^2}[1+\frac{{\mathrm{v}}_{\mathrm{y}0}^2}{{\mathrm{v}}_{\mathrm{x}0}^2}]$$$$\Rightarrow \mathrm{K}-\mathrm{t}\mathrm{graph}\mathrm{is}\mathrm{a}\mathrm{parabola}$$$$\mathrm{K}=\frac{1}{2}\mathrm{m}[{({\mathrm{v}}_{\mathrm{y}0}-\mathrm{gt})}^2+{\mathrm{v}}_{\mathrm{x}0}^2]$$$$\mathrm{so}\mathrm{K}-\mathrm{t}\mathrm{graph}\mathrm{is}\mathrm{a}\mathrm{parabola}.$$$$\mathrm{statements}\left(1\right)\mathrm{and}\left(3\right)\mathrm{are}\mathrm{true}.$$

Commented by Tinkutara last updated on 12/Aug/17

$$\mathrm{Thank}\mathrm{you}\mathrm{very}\mathrm{much}\mathrm{Sir}!$$

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