A certain lake is proposed as a landing area for a large jet aircraft. The touch down speed of 100 km/hr upon contact with water is to be reduced to 20 km/hr in a distance of 0.45 km. If the deceleration is proportional to square of velocity of aircraft through water, a = -kv. Find the value of design parameter k, which would be a measure of size and shape of landing gear vanes that plow through the water. Also find the time't' elapsed during the specific time interval.