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Found in: Page 150

### Physics For Scientists & Engineers

Book edition 9th Edition
Author(s) Raymond A. Serway, John W. Jewett
Pages 1624 pages
ISBN 9781133947271

# A submarine dives from the water surface at an angle of 300 below the horizontal, following a straight path 50m long. How far is the submarine then below the water surface? (a) 50m (b) 50m/sin300 (c) (50m)sin300(d) (50m)cos300 (e) none of those answers.

The correct option is (c).

See the step by step solution

## Step 1: Definition of sine and cosine

The sine and cosine of an angle are trigonometric functions. In the context of a right triangle, the sine and cosine of an acute angle are defined as follows: for the specified angle, the sine is the ratio of the length of the opposite side to the length of the triangle's longest side (the hypotenuse), and the cosine is the ratio of the length of the adjacent leg to the hypotenuse.

## Step 2: Explanation for the correct option

As per the above figure and the definition of sine and cosine, $cos\theta =\frac{{A}_{x}}{A}andsin\theta =\frac{{A}_{y}}{A}.$

Hence the components of $\stackrel{\to }{A}$are localid="1663659516194" ${A}_{x}=Acos\theta and{A}_{y}=Asin\theta .$

A submarine takes a straight course 50m long from the water's surface at an angle of 300 below the horizontal.

The submarine below the water surface is calculated as

$\mathrm{sin}30°=\frac{y}{50m}\phantom{\rule{0ex}{0ex}}y=\left(50 m\right)\mathrm{sin}30°$

So option (c) is correct.

## Step 3: Explanation for option (a)

By calculation it is known that the submarine is 50m(sin300) below the water's surface.

So, option (a) 50m is incorrect.

## Step 4: Explanation for option (b)

By calculation it is known that the submarine is (50m)sin300 below the water's surface.

So, option (b) 50m/sin300 is incorrect.

## Step 5: Explanation for option (d)

By calculation it is known that the submarine is (50m)sin300 below the water's surface.

So, option (d) (50m)sin300 is incorrect.

## Step 6: Explanation for option (e)

By calculation it is known that the submarine is 50m sin300 below the water's surface.

Since, option (c) is correct, which implies that option (e) is incorrect