A cylinder is rolling on a horizontal plane surface. Given that the...

For a cylinder rolling on a horizontal surface, the condition for pure rolling is $v_{cm} = \omega R$.

The velocity of the highest point is the vector sum of the translational velocity of the centre of mass and the tangential velocity due to rotation.

At the highest point, both velocities are in the same direction.

$v_{top} = v_{cm} + \omega R = 2v_{cm}$

Given $v_{cm} = 25 \text{ m/s}$, substituting the value:

$v_{top} = 2 \times 25 = 50 \text{ m/s}$