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It's nighttime, and you've dropped your goggles into a 2.8-m-deep swimming pool. If you hold a laser pointer 1.1 m above the edge of the pool, you can illuminate the goggles if the laser beam enters the water 2.1 m from the edge. How far are the goggles from the edge of the pool? Express your answer to two significant figures and include the appropriate units.

User Diya
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1 Answer

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To find the answer, we can use the Pythagorean Theorem: a² + b² = c², where 'c' is the hypotenuse (in this case it's the distance at which the light enters the water), 'a' is one of the sides (in this case it's the horizontal distance from the goggles to the edge of the pool), and 'b' is the other side (in this case it's the difference between the depth of the goggles and the height of the laser).

Let's start by calculating the difference between the depth of the goggles and the height of the laser.

The goggles are 2.8 m deep and the laser is 1.1 m above the pool so,

2.8 m - 1.1 m = 1.7 m

Now that we know the difference in height, we need to use the Pythagorean Theorem to find the horizontal distance from the goggles to the edge of the pool. We know that 'c' (light_water_entry) is 2.1 m and 'b' (depth_diff), as calculated just now, is 1.7 m.

So, the equation would be:

a² = c² - b² = (2.1 m)² - (1.7 m)²

Upon calculation, we find the horizontal distance 'a' (also known as goggles_distance) by taking the square root of the result from the equation above:

a = √[((2.1 m)² - (1.7 m)²)]

This results to approximately 1.23 m after rounding to two significant figures.

Therefore, the goggles are approximately 1.23 m from the edge of the pool.

User BKK
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