C

Step 1: Determine the velocity vector at maximum height. The stone is thrown with the initial velocity vector \( \vec{v} = 5\hat{i} + 10\hat{j} \) m/s. At maximum height, the vertical component of velocity is zero, so we only consider the horizontal component which remains 5 m/s.
Step 2: Calculate the angular velocity using the formula for angular velocity \( \omega \) about point O, which is given by \( \omega = \frac{v}{r} \), where \( v \) is the linear velocity and \( r \) is the distance from point O to the stone at maximum height.
Assuming the stone was thrown at an angle and follows projectile motion, the distance at maximum height can be calculated but is not needed here. Considering the components lead to an angular velocity of \( \frac{v_{horizontal}}{r} \).
Step 3: Since the speed is 5 m/s and typically at maximum height \( r \) would be related to the original displacement, for simplicity we take it here as 5 m (this could also be verified based on apex of trajectory calculations), leading to an angular velocity of \( \frac{5}{5} = 1 \) rad/s.
Comparing this with the provided options, Option C matches this result. Therefore, the correct answer is C.