# Q 5.     A stone is thrown in a vertically upward direction with a velocity of $5\ m s^{-1}$. If the acceleration of the stone during its motion is $10\ m s^{-2}$ in the downward direction, what will be the height attained by the stone and how much time will it take to reach there?

H Harsh Kankaria

Taking upward direction as positive (+) direction:

Given,

$u = 5\ ms^{-1}$

$a = -10\ ms^{-2}$         (This is due to gravitational force!)

The stone will move up until its velocity becomes zero.

$\therefore v = 0\ ms^{-1}$

We know, $v^2 = u^2 + 2as$

$\\ \implies 0^2 = 5^2 + 2(-10)s \\ \implies 20 s = 25 \\ \implies s = 1.25\ m$

Therefore, the stone reaches to a height of $1.25\ m$

Now,

We know, $v = u + at$

$\\ \implies 0 = 5 + (-10)t \\ \implies t = 0.5\ s$

Therefore, the time taken by the stone to reach the maximum height is $0.5\ s$.

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