$3.)$ A storm washed away sand from a beach, causing the edge of the water to get closer to a nearby road. The rate at which the distance between the road and the edge of the water was changing during the storm is modeled by $f(t)=\sqrt[\phantom{2}]{t}+cost-3$ meters per hour, $t$ hours after the storm began. The edge of the water was $35$ meters from the road when the storm began, and the storm lasted $5$ hours. The derivative of $f(t)$ is $f^{\text{'}}(t)=\frac{1}{2\sqrt[\phantom{2}]{t}}-sint.$

At what time during the $5$ hours of the storm was the distance between the road and the edge of the water decreasing most rapidly? Justify your answer.