To solve this problem, we need to determine the swimmer's total displacement after 5 minutes by considering both her own velocity and the velocity of the current.

Step 1: Decompose the current's velocity

The current is moving at 8 m/s at an angle of 300°. To break this down into its horizontal ($x$) and vertical ($y$) components, we use trigonometry:

• $V_{x} = 8 \cos(300^\circ)$
• $V_{y} = 8 \sin(300^\circ)$

Since $\cos(300^\circ) = \frac{1}{2}$ and $\sin(300^\circ) = -\frac{\sqrt{3}}{2}$, we get:

• $V_{x} = 8 \times \frac{1}{2} = 4 \, \text{m/s}$
• $V_{y} = 8 \times -\frac{\sqrt{3}}{2} = -4\sqrt{3} \approx -6.93 \, \text{m/s}$

Step 2: Combine the swimmer's velocity and the current's velocity

The swimmer is moving north (in the positive $y$-direction) at 5 m/s, so her total velocity in the $y$-direction is the sum of her velocity and the $y$-component of the current:

• $V_{y, \text{total}} = 5 + (-6.93) = -1.93 \, \text{m/s}$

In the $x$-direction, only the current is contributing to the velocity:

• $V_{x, \text{total}} = 4 \, \text{m/s}$

Step 3: Find the total displacement after 5 minutes

The swimmer is moving for 5 minutes, which is 300 seconds. Now, we calculate her displacement in the $x$ and $y$ directions:

• $D_{x} = V_{x, \text{total}} \times t = 4 \times 300 = 1200 \, \text{m}$
• $D_{y} = V_{y, \text{total}} \times t = -1.93 \times 300 = -579 \, \text{m}$

Step 4: Calculate the total displacement

The total displacement is the magnitude of the resultant vector:

$D_{\text{total}} = \sqrt{D_{x}^2 + D_{y}^2} = \sqrt{1200^2 + (-579)^2} = \sqrt{1440000 + 335241} = \sqrt{1775241} \approx 1332.26 \, \text{m}$

Thus, the swimmer is approximately 1332.26 meters from her starting point after 5 minutes.

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Would you like further details or have any questions?

Here are 5 related questions:

1. How would the problem change if the current's velocity was 10 m/s?
2. What if the swimmer were swimming south instead of north?
3. How would you calculate the time taken to reach a certain distance?
4. How would the calculation change if the current's direction was 45 degrees?
5. How does the angle of the current affect the displacement?

Tip: Always break down vectors into components when dealing with motion at angles.