To find the velocity of the stone just before reaching the ground, we need to consider the effects of gravity. Since air resistance is ignored, the only force acting on the stone is the force due to gravity.
The stone is thrown upward with an initial velocity of 20 m/s, and we assume the acceleration due to gravity to be 10 m/s².
When the stone reaches its highest point, its velocity will momentarily be zero. After that, it starts falling downward, and its velocity increases due to the acceleration of gravity.
To find the velocity just before reaching the ground, we can use the following kinematic equation:
v² = u² + 2as
where: v = final velocity (which we need to find) u = initial velocity (20 m/s, but with a negative sign because it is directed upward) a = acceleration (-10 m/s², with a negative sign because it is directed downward) s = displacement (the distance covered by the stone)
We need to find the displacement s for the stone to reach the ground. The stone was initially thrown upward, and it will reach the ground when its displacement is equal to zero. So, the stone's displacement will be zero when it reaches the ground.
Plugging the values into the kinematic equation:
v² = (20 m/s)² + 2(-10 m/s²)(0) v² = 400 m²/s²
Taking the square root of both sides:
v = ± √400 m/s v = ± 20 m/s
Since the velocity is a vector quantity, it can have both positive and negative values, indicating the direction. In this case, the positive value indicates the stone's upward velocity, while the negative value indicates the stone's downward velocity.
Therefore, the stone's velocity just before reaching the ground is -20 m/s, indicating that it is moving downward.