Kinematics

JEE Main level, single correct, medium

279 of 308

Question 279 of 308

If t1t_1 and t2t_2 are the times of flight of two particles having the same initial velocity uu and range R\mathrm{R} on the horizontal, then t12+t22\mathrm{t}_1^2+\mathrm{t}_2^2 is equal to

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Answer: (B) 4u2g2\frac{4 u^2}{g^2}

t1=2usin⁡αg,t2=2usin⁡βg\mathrm{t}_1=\frac{2 \mathrm{u} \sin \alpha}{\mathrm{g}}, \mathrm{t}_2=\frac{2 \mathrm{u} \sin \beta}{\mathrm{g}} where α+β=90∘\alpha+\beta=90^{\circ}
∴t12+t22=4u2 g2\therefore \mathrm{t}_1^2+\mathrm{t}_2^2=\frac{4 \mathrm{u}^2}{\mathrm{~g}^2}

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