Question

A diver explores a shallow reef off the coast of Belize. She initially swims 90.0 m north, makes a turn to the east and continues for 200.0 m, then follows a big grouper for 80.0 m in the direction 30° north of east. In the meantime, a local current displaces her by 150.0 m south. Assuming the current is no longer present, in what direction and how far should she now swim to come back to the point where she started?

a) 40° south of west, 190 m
b) 50° north of east, 80 m
c) 30° east of south, 70 m
d) 20° west of north, 30 m

Answer 1

By computing the resultant vector from the diver's movements and the displacement by current, it is found that she must swim 70 m in the direction 30° east of south to return to her starting point.

Step-by-step explanation:

The problem presented is a classic example of a vector addition and displacement problem in physics. The steps the diver takes represent individual vector quantities, which when combined give us her total displacement. To solve for the direction and magnitude of the path the diver must swim to return to her starting point, we need to calculate the resultant vector from her individual displacements.

Firstly, we break down the path followed by the diver into its component vectors:

• 90.0 m north
• 200.0 m east
• 80.0 m at 30° north of east
• 150.0 m south (due to the current)

After calculating the sum of these vectors, we need to determine the resultant vector that will bring the diver back to her starting point from her final position. This involves finding the magnitude and the direction of the vector that is the inverse of the sum of her displacement vectors. This resultant vector is the path the diver needs to take to return to her starting point.

The correct answer to this question is that the diver should swim in the direction 30° east of south, and the distance is 70 m, making the correct option 'c) 30° east of south, 70 m'.