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Free Fall

A body underg...

Question

A body undergoes a free fall. Taking downward direction as +ve $Y$ direction and $Y_{o}$ is the initial position, $Y$ coordinate at any time $t$ is given by

Y_{o} - Y = \frac{1}{2} g t^{2}

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Y_{o} = \frac{1}{2} g t^{2}

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Y_{o} - Y = - \frac{1}{2} g t^{2}

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Y_{o} + Y = \frac{1}{2} g t^{2}

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Solution

The correct option is C $Y_{o} - Y = - \frac{1}{2} g t^{2}$
Initial position is $Y_{o}$ and downward is +ve $Y$ direction so gravity $(g)$ is acting in positive direction.
Displacement, $s = u t + \frac{1}{2} a t^{2}, u = 0 a n d a = g$
We get, $s = 0 + \frac{1}{2} g t^{2} = \frac{1}{2} g t^{2}$
So, let the final position be $Y = Y_{o} + s = Y_{o} + \frac{1}{2} g t^{2}$
$∴ Y_{o} - Y = - \frac{1}{2} g t^{2}$

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