To find the initial speed of the stone, we can analyze the vertical motion of the stone when it reaches its maximum height. We'll use the kinematic equation for vertical motion:
v_f^2 = v_i^2 + 2 * a * Δy
where: v_f is the final vertical velocity (which is 0 m/s at the maximum height), v_i is the initial vertical velocity (the value we need to find), a is the acceleration due to gravity (-9.8 m/s^2), Δy is the change in vertical position (which is 24 m).
Since the stone is thrown upward, the initial vertical velocity (v_i) is positive. Plugging in the known values, we get:
0^2 = v_i^2 + 2 * (-9.8 m/s^2) * 24 m
0 = v_i^2 - 470.4
v_i^2 = 470.4
v_i = √470.4
v_i ≈ 21.68 m/s
Therefore, the initial speed of the stone was approximately 21.68 m/s.