A drone's vertical displacement $h(t)$, measured in metres, is modelled by the polynomial $h(t)=2t^3-k{t}^2+5t+11$, where $t\ge 0$ is the time in seconds and $k$ is a constant. Given that the remainder when $h(t)$ is divided by $(t-2)$ is $17$, calculate the value of $k$.