Question

In an attempt to escape his island, Gilligan builds a raft and sets to sea. The wind shifts a great deal during the day, and he is blown along the following straight lines:

1. 2.50 {km} 45.0^∘ north of west
2. 4.70 {km} 60.0^∘ south of east
3. 1.30 {km} 25.0^∘ south of west
4. 5.10 {km} straight east
5. 1.70 {km} 5.00^∘ east of north
6. 7.20 {km} 55.0^∘ south of west
7. 2.80 {km} 10.0^∘ north of east

What is his final position relative to the island?

MCQ Options:
a) 2.50 {km} east
b) 2.50 {km} west
c) 2.50 {km} north
d) 2.50 {km} south

Answer 1

Gilligan's final position can be determined by resolving each leg of his journey into north/south and east/west components and summing them. This requires using trigonometry to decompose the vectors and find the resultant displacement vector.

Step-by-step explanation:

To determine Gilligan's final position relative to the island, we need to break down each component of his journey into north/south and east/west components and then add those components up to find the resultant vector. This process involves using trigonometric functions to resolve each leg of Gilligan’s journey into its components.

• First leg (2.50 km, 45.0° north of west): decomposed into north and west components.
• Second leg (4.70 km, 60.0° south of east): decomposed into south and east components.
• Third leg (1.30 km, 25.0° south of west): decomposed into south and west components.
• Fourth leg (5.10 km, straight east): no decomposition needed, already a pure east component.
• Fifth leg (1.70 km, 5.00° east of north): decomposed into north and east components.
• Sixth leg (7.20 km, 55.0° south of west): decomposed into south and west components.
• Seventh leg (2.80 km, 10.0° north of east): decomposed into north and east components.

After calculating and summing all these components, we will be able to find Gilligan's final displacement from his starting point, which will indicate his final position with respect to the island.