Solid homogeneous cylinders $530$ mm high and $200$ mm in diameter are supported by a flat conveyor belt which moves horizontally. If

the speed of the belt increases according to $v=2\mathrm{.}88+0\mathrm{.}63t^2\frac{m}{s},$ where $t$ is the time in seconds measured from the instant the

increase begins, calculate the value of $t$ for which the cylinders begin to tip over. Cleats on the belt prevent the cylinders from slipping.