Question

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?

Answer 1

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Given :

Initial Velocity of the stone (u) = 5m/s

Final Velocity of the stone (v) = 0 (since the stone comes to rest when it reaches maximum height)

Acceleration of the stone (a) = acceleration due to gravity (g) = 10m/s^2 (in a downward direction)

There will be a change in the sign of acceleration because the stone is being thrown upwards, acceleration (a) = -10m/s^2

Solution:

Let s be the maximum height attained by the stone in the time t

According to the first equation of motion:

v = u + at

0 = 5 + (-10)t

t = $\frac{ - 5}{10}$

= 0.5s

According to the 3rd equation

v^2 = u^2 + 2as

0^2 = 5^2 + 2 (-10)s

s= $\frac{ - 5 {}^{2} }{20}$

= 1.25m