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Motion — Science STD 9 — Question

Rajasthan BoardEnglish MediumSTD 9ScienceMotion3 Marks
Question
Two stones are thrown vertically upwards simultaneously with their initial velocities $u_1$ and $u_2$ respectively. Prove that the heights reached by them would be in the ratio of $\text{u}_1^2:\text{u}_2^1$ (Assume upward acceleration is $–g$ and downward acceleration to be $+g).$
✓

Answer

We know for upward motion,  $\text{v}^2=\text{u}^2-2\text{gh}$ or $\text{h}=\frac{\text{u}^2-\text{v}^2}{2\text{g}}$
But at highest point $\text{v}=0$
Therefore, $\text{h}=\frac{\text{u}^2}{\text{g}}$
For first ball, $\text{h}_1=\text{u}_1\frac{2}{2\text{g}}$
And for second ball, $\text{h}_2=\frac{\text{u}^2_2}{2\text{g}}$
Thus, $\frac{\text{h}_1}{\text{h}_2}=\frac{\text{u}_1^2/2\text{g}}{\text{u}_2^2/2\text{g}}=\frac{\text{u}_1^1}{\text{u}_2^2}$ or $\text{h}_1:\text{h}_2=\text{u}_1^2:\text{u}_2^2$

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