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

Question

Dr. Abubacker · Accepted Answer

(d) The equation of motion
$\left( \frac{u}{2} ight)^{2} = u^{2} - 2g\ (AO)$
$2g 	imes AO = u^{2} - \frac{u^{2}}{4} = \frac{3u^{2}}{4}$
$\ \ \ \ \ \ \ \ \ \ AO = \frac{3u^{2}}{8g}$
When particle will reach at point $B$
$\left( \frac{u}{3} ight)^{2} = u^{2} - 2g(OB)$
$\ \ \ OB = \frac{8u^{2}}{18g}$
When particle will reach at point $C$
$\left( \frac{u}{4} ight)^{2} = u^{2} - 2g\ (OC)$
$OC = \frac{15u^{2}}{32g}$
$AB = OB - OA = \frac{u^{2}}{g}\left\lbrack \frac{8}{18} - \frac{3}{8} ightbrack = \frac{5u^{2}}{72g}$
$BC = OC - OB = \frac{u^{2}}{g}\left\lbrack \frac{15}{32} - \frac{8}{18} ightbrack$
The ratio, $\frac{AB}{BC} = \frac{20}{7}$
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Q. A body is thrown vertically up with a velocity $u.$ It passes three points $A,\ B\ and\ C$ in its upward journey with velocities $\frac{u}{2},\frac{u}{3}and\frac{u}{4}$ respectively. The ratio of the separations between points $A\ and\ B$ between $B\ and\ C,\ ie,\frac{AB}{BC}$ is

Explanation

Reviewed by Dr. Abubacker

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