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STD 11 - 3.2. motion in plane — NEET STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceNEETSTD 11 - 3.2. motion in plane4 Marks
Question
Two balls are projected from the same point simultaneously.First ball is projected vertically upwards and the second ball at an angle of projection $60^o$ to the ground level. Both the balls reach the ground simultaneously. The ratio of their velocities are
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Answer

time of flight $\mathrm{T}_{1}=\frac{2 \mathrm{u}_{1}}{\mathrm{g}}, \quad \mathrm{T}_{2}=\frac{2 \mathrm{u}_{2} \sin 60^{\circ}}{\mathrm{g}}$

Time of flights are equal, so $\mathrm{T}_{2}=\mathrm{T}_{1}$ $\frac{2 u \sqrt{3}}{2 g}=\frac{2 u_{1}}{g}=u_{2} \sqrt{3}=2 u_{1} \Rightarrow \frac{u_{1}}{u_{2}}=\frac{\sqrt{3}}{2}$

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