Final answer:
To calculate the contact's estimated speed, we determine the distance it covered in miles and divide by the time taken in hours. The contact traveled 2 miles in 1/5 hour, resulting in an estimated speed of 10 miles per hour. When adjusted for the student's own ship speed, the contact's speed through the water is approximately 15.7539 miles per hour.
Step-by-step explanation:
To determine the estimated speed of the contact which is a vessel or object that a ship detects on its radar, we can use the formula for speed:
Speed equals distance divided by time. In this scenario, the contact is initially 10 miles astern and after 12 minutes it is 8 miles astern. Therefore, the contact has covered a distance of 2 miles (10 miles - 8 miles) in 12 minutes, which constitutes 1/5 of an hour (12 minutes is 12/60 hours).
Using the speed formula: Speed = Distance/Time
Speed = 2 miles / (1/5 hour) = 2 miles × 5 = 10 miles/hour
Since the student's own ship is traveling at 5 knots and considering that 1 knot equals to 1.15078 miles per hour, the ship's speed in miles per hour is 5 knots × 1.15078 = 5.7539 miles/hour. The contact's estimated speed in miles per hour is higher than that of the student's ship, meaning the contact is catching up.
To find the actual speed the contact is moving through the water, we'd have to add the student's ship's speed to the approach speed calculated:
Contact's speed through the water = Contact's estimated speed + Student's ship speed
Contact's speed through the water = 10 mph + 5.7539 mph = 15.7539 miles per hour.