To determine the approximate speed of the stone when it turns back to the ground, we need to consider the motion of the stone when it reaches its maximum height. At the highest point of its trajectory, the stone momentarily comes to rest before descending back down.
Assuming there is no air resistance and neglecting any other external forces, we can analyze the stone's motion using the principles of projectile motion. The key concept to consider is that the vertical component of the stone's velocity decreases due to the acceleration of gravity while it rises and increases in the opposite direction when it falls.
Given that the initial speed of the stone is 20 m/s, we can determine the speed of the stone when it turns back to the ground by considering its vertical motion. At the highest point, the vertical component of the velocity is zero.
Using the equation for vertical motion:
v^2 = u^2 + 2as
where v = final vertical velocity (0 m/s at the highest point) u = initial vertical velocity (20 m/s) a = acceleration due to gravity (-9.8 m/s^2, taking the negative sign since it opposes the upward motion) s = displacement (height)
Rearranging the equation:
0^2 = (20 m/s)^2 + 2(-9.8 m/s^2)s
400 m^2/s^2 = -19.6 m/s^2 * s
s ≈ -400 m^2/s^2 / -19.6 m/s^2
s ≈ 20.41 m
Therefore, the stone reaches a maximum height of approximately 20.41 meters.
To find the speed of the stone when it turns back to the ground, we can use the same equation, but this time with the displacement equal to the initial height (20.41 meters) since the stone is back at the same level.
v^2 = u^2 + 2as
v^2 = 0^2 + 2(-9.8 m/s^2)(20.41 m)
v^2 ≈ -400 m^2/s^2
v ≈ √(-400 m^2/s^2)
v ≈ ±20 m/s
The approximate speed of the stone at the point of turning back to the ground is approximately 20 m/s. The negative sign indicates that the stone is moving downward.