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Q12 OQ

Expert-verifiedFound in: Page 150

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 30 ^{0}**

**(a) 50m**** (b) 50m/sin30 ^{0}**

The correct option is (c).

**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.**

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 $\overrightarrow{A}$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 30^{0} below the horizontal.

The submarine below the water surface is calculated as

$\mathrm{sin}30\xb0=\frac{y}{50m}\phantom{\rule{0ex}{0ex}}y=(50\hspace{0.33em}m)\mathrm{sin}30\xb0$

So option (c) is correct.

By calculation it is known that the submarine is 50m(sin30^{0}) below the water's surface.

So, option (a) 50m is incorrect.

By calculation it is known that the submarine is (50m)sin30^{0} below the water's surface.

So, option (b) 50m/sin30^{0} is incorrect.

By calculation it is known that the submarine is (50m)sin30^{0} below the water's surface.

So, option (d) (50m)sin30^{0} is incorrect.

By calculation it is known that the submarine is 50m sin30^{0} below the water's surface.

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

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