A heavy particle is suspended by a string of length l. The particle is given a horizontal velocity $v_{0}$ . The string becomes slack at some angle and the particle proceeds on a parabola. Find the value of $v_{0}$ if the particle passes through the point of suspension.

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A heavy particle is suspended by a string of length l. The particle is given a horizontal velocity $v_{0}$ . The string becomes slack at some angle and the particle proceeds on a parabola. Find the value of $v_{0}$ if the particle passes through the point of suspension.

$m g c o s θ = \frac{m v^{2}}{l}$
$\Rightarrow v^{2} = g l c o s θ \to (1)$
By coE
$\frac{1}{2} m v_{0}^{2} = \frac{1}{2} m v^{2} + m b l (1 + c o s θ) \to (2)$
solving $v_{0}^{2} = g l (2 + 3 c o s θ)$
Now, $l s i n θ = v c o s θ t$
and $- l c o s θ = v s i n θ t - \frac{1}{2} g t^{2}$

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A heavy particle is suspended by a string of length l. The particle is given a horizontal velocity v0. The string becomes slack at some angle and the particle proceeds on a parabola. Find the value of v0 if the particle passes through the point of suspension.

A heavy particle is suspended by a string of length l. The particle is given a horizontal velocity $v_{0}$ . The string becomes slack at some angle and the particle proceeds on a parabola. Find the value of $v_{0}$ if the particle passes through the point of suspension.