A body is thrown vertically up with a velocity u. It passes three points A, Band e in its upward journey with velocities u2,u3 and u4, respectively. The ratio of the separations between points A and B and between B and C, i.e. ABBC is

A⇒u24-u2=-2gh1B⇒u29-u2=-2gh2C⇒u216-u2=-2gh3∴ AB=u22g89-34=u22g·536 BC=u22g1516-89=u22g·7144∴ ABBC=536×1447=207

A body is thrown vertically up with a velocity u. It passes three points A, Band e in its upward journey with velocities u2,u3 and u4, respectively. The ratio of the separations between points A and B and between B and C, i.e. ABBC is

A⇒u24-u2=-2gh1B⇒u29-u2=-2gh2C⇒u216-u2=-2gh3∴ AB=u22g89-34=u22g·536 BC=u22g1516-89=u22g·7144∴ ABBC=536×1447=207

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A body is thrown vertically up with a velocity u. It passes three points A, Band e in its upward journey with velocities $\frac{u}{2}, \frac{u}{3} and \frac{u}{4}$ , respectively. The ratio of the separations between points A and B and between B and C, i.e. $\frac{AB}{BC}$ is

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$\frac{10}{7}$

$\frac{20}{7}$

answer is D.

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$A \Rightarrow \frac{u^{2}}{4} - u^{2} = - 2 g h_{1}$

$B \Rightarrow \frac{u^{2}}{9} - u^{2} = - 2 g h_{2}$

$C \Rightarrow \frac{u^{2}}{16} - u^{2} = - 2 g h_{3}$

$∴$ $A B = \frac{u^{2}}{2 g} (\frac{8}{9} - \frac{3}{4}) = \frac{u^{2}}{2 g} \cdot \frac{5}{36}$

$B C = \frac{u^{2}}{2 g} (\frac{15}{16} - \frac{8}{9}) = \frac{u^{2}}{2 g} \cdot \frac{7}{144}$

$∴$ $\frac{A B}{B C} = \frac{5}{36} \times \frac{144}{7} = \frac{20}{7}$

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A body is thrown vertically up with a velocity u. It passes three points A, Band e in its upward journey with velocities u2,u3 and u4, respectively. The ratio of the separations between points A and B and between B and C, i.e. ABBC is

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A body is thrown vertically up with a velocity u. It passes three points A, Band e in its upward journey with velocities $\frac{u}{2}, \frac{u}{3} and \frac{u}{4}$ , respectively. The ratio of the separations between points A and B and between B and C, i.e. $\frac{AB}{BC}$ is