Question

A ship leaves port at 10am traveling north at 35knots. 3 hours later the ship changes course N 65 degrees E and travels for one hour? How far from the port is the ship at 2pm? How far from the port will it be at 3pm?

Answer 1

Answer: 2pm = 95.6 knots

3pm = 98.6 knots

Explanation:

Use the Law of Cosines:

b² = a² + c² - 2ac·cos B

At 2pm, the boat traveled (35 × 3)knots North and (35 × 1)knots NE:

b² = a² + c² - 2ac·cos B

b² = 35² + 105² - 2(35)(105)·cos 65°

b² = 1225 + 11025 - 7350(0.4226)

b² = 9143

b = 95.6

At 3pm, the boat traveled (35 × 3)knots North and (35 × 2)knots NE:

b² = a² + c² - 2ac·cos B

b² = 70² + 105² - 2(70)(105)·cos 65°

b² = 4900 + 11025 - 14700(0.4226)

b² = 9712.5

b = 98.6