Answer
427.8k+ views
Hint:First,calculate distance travelled by using the given terms such as velocity. Here, distance travelled by the plane and the shell fired are the same. So equate them to get the required distance and then find the value of the angle made by the man to fire.
Complete step by step answer:
Let us draw the figure, to understand quickly and properly,
Velocity of the plane, $v = 300m/s$
Let initial angle at which man fires is $ = \theta $
Let P be the point at which it hit an enemy plane.
Initial speed of the fire shell, $v = 600m/s$
Elevation is given at $2km$
Let “t” be the time at which it hit,
Therefore distance travelled by plane in the horizontal direction$ = 300 \times t$ ....... (a)
Shell travelled in the x-direction =$ = 600 \times \cos \theta \times t$ ........ (b)
Now, equation (a) and (b) are equal as they travel the equal distance.
$300 \times t = 600 \times \cos \theta \times t$
Simplify the above equation –
Take “t” common from both the sides of the equation and remove them.
$300 = 600\cos \theta $
Make unknown angle the subject –
$
\cos \theta = \dfrac{{300}}{{600}} \\
\Rightarrow \cos \theta = \dfrac{1}{2} \\
\Rightarrow \theta = {\cos ^{ - 1}}\left( {\dfrac{1}{2}} \right) \\
\Rightarrow \theta = 60^\circ \\
$
It makes angle, $\theta = 60^\circ $therefore, vertical angle is $ = 90^\circ - \theta = 90^\circ - 60^\circ = 30^\circ $
Therefore, the required answer is - The gun should be fired at an angle $30^\circ $ from the vertical so as to hit the plane.
Hence, from the given multiple choices – option D is the correct answer.
Note:Remember all the different trigonometric angles which are the angles given by the ratios of the trigonometric functions. The most important trigonometric angles are $0^\circ ,{\text{ 3}}0^\circ ,\;45^\circ ,{\text{ 6}}0^\circ {\text{ and 9}}0^\circ $. Remember the values of these angles for quick substitution for further simplification.
Complete step by step answer:
Let us draw the figure, to understand quickly and properly,
![seo images](https://www.vedantu.com/question-sets/3878bdd8-8edf-4334-bcce-38f3b5fd8c97417638117394970818.png)
Velocity of the plane, $v = 300m/s$
Let initial angle at which man fires is $ = \theta $
Let P be the point at which it hit an enemy plane.
Initial speed of the fire shell, $v = 600m/s$
Elevation is given at $2km$
Let “t” be the time at which it hit,
Therefore distance travelled by plane in the horizontal direction$ = 300 \times t$ ....... (a)
Shell travelled in the x-direction =$ = 600 \times \cos \theta \times t$ ........ (b)
Now, equation (a) and (b) are equal as they travel the equal distance.
$300 \times t = 600 \times \cos \theta \times t$
Simplify the above equation –
Take “t” common from both the sides of the equation and remove them.
$300 = 600\cos \theta $
Make unknown angle the subject –
$
\cos \theta = \dfrac{{300}}{{600}} \\
\Rightarrow \cos \theta = \dfrac{1}{2} \\
\Rightarrow \theta = {\cos ^{ - 1}}\left( {\dfrac{1}{2}} \right) \\
\Rightarrow \theta = 60^\circ \\
$
It makes angle, $\theta = 60^\circ $therefore, vertical angle is $ = 90^\circ - \theta = 90^\circ - 60^\circ = 30^\circ $
Therefore, the required answer is - The gun should be fired at an angle $30^\circ $ from the vertical so as to hit the plane.
Hence, from the given multiple choices – option D is the correct answer.
Note:Remember all the different trigonometric angles which are the angles given by the ratios of the trigonometric functions. The most important trigonometric angles are $0^\circ ,{\text{ 3}}0^\circ ,\;45^\circ ,{\text{ 6}}0^\circ {\text{ and 9}}0^\circ $. Remember the values of these angles for quick substitution for further simplification.
Recently Updated Pages
Mark and label the given geoinformation on the outline class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
When people say No pun intended what does that mea class 8 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Name the states which share their boundary with Indias class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give an account of the Northern Plains of India class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Advantages and disadvantages of science
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
10 examples of evaporation in daily life with explanations
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
How do you graph the function fx 4x class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)