First slide

Vertical projection from ground

Question

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

Moderate

A

1
B

2
C

$\frac{10}{7}$
D

$\frac{20}{7}$

Solution

$A \Rightarrow \frac{u^{2}}{4} - u^{2} = - 2 g h_{1}$
$B \Rightarrow \frac{u^{2}}{9} - u^{2} = - 2 g h_{2}$
$C \Rightarrow \frac{u^{2}}{16} - u^{2} = - 2 g h_{3}$
$∴$ $A B = \frac{u^{2}}{2 g} (\frac{8}{9} - \frac{3}{4}) = \frac{u^{2}}{2 g} \cdot \frac{5}{36}$
$B C = \frac{u^{2}}{2 g} (\frac{15}{16} - \frac{8}{9}) = \frac{u^{2}}{2 g} \cdot \frac{7}{144}$
$∴$ $\frac{A B}{B C} = \frac{5}{36} \times \frac{144}{7} = \frac{20}{7}$

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