English
Karnataka Board PUCPUC Science Class 11

A Mosquito Net Over a 7 Ft × 4 Ft Bed is 3 Ft High. the Net Has a Hole at One Corner of the Bed Through Which a Mosquito Enters the Net. It Flies and Sits at the Diagonally Opposite

Advertisements
Advertisements

Question

A mosquito net over a 7 ft × 4 ft bed is 3 ft high. The net has a hole at one corner of the bed through which a mosquito enters the net. It flies and sits at the diagonally opposite upper corner of the net. (a) Find the magnitude of the displacement of the mosquito. (b) Taking the hole as the origin, the length of the bed as the X-axis, it width as the Y axis, and vertically up as the Z-axis, write the components of the displacement vector.

Answer in Brief
Sum
Advertisements

Solution

Displacement vector of the mosquito,

\[\vec{r} = 7 \hat {i} + 4 \hat {i} + 3 \hat {k}\]
(a) Magnitude of displacement
\[= \sqrt{7^2 + 4^2 + 3^2}\]
\[= \sqrt{74} \text { ft }\]
(b) The components of the displacement vector are 7 ft, 4 ft and 3 ft along the X, Y and Z-axes, respectively.
shaalaa.com
  Is there an error in this question or solution?
Chapter 2: Physics and Mathematics - Exercise [Page 29]

APPEARS IN

HC Verma Concepts of Physics Volume 1 and 2 [English]
Chapter 2 Physics and Mathematics
Exercise | Q 9 | Page 29

RELATED QUESTIONS

“Every great physical theory starts as a heresy and ends as a dogma”. Give some examples from the history of science of the validity of this incisive remark


If all the terms in an equation have same units, is it necessary that they have same dimensions? If all the terms in an equation have same dimensions, is it necessary that they have same units?


Suggest a way to measure the thickness of a sheet of paper.


\[\int\frac{dx}{\sqrt{2ax - x^2}} = a^n \sin^{- 1} \left[ \frac{x}{a} - 1 \right]\] 
The value of n is


The height of mercury column in a barometer in a Calcutta laboratory was recorded to be 75 cm. Calculate this pressure in SI and CGS units using the following data : Specific gravity of mercury = \[13 \cdot 6\] , Density of \[\text{ water} = {10}^3 kg/ m^3 , g = 9 \cdot 8 m/ s^2\] at Calcutta. Pressure
= hpg in usual symbols.


Let x and a stand for distance. Is
\[\int\frac{dx}{\sqrt{a^2 - x^2}} = \frac{1}{a} \sin^{- 1} \frac{a}{x}\] dimensionally correct?


Is a vector necessarily changed if it is rotated through an angle?


Can you have  \[\vec{A} \times \vec{B} = \vec{A} \cdot \vec{B}\] with A ≠ 0 and B ≠ 0 ? What if one of the two vectors is zero?


A vector \[\vec{A}\] points vertically upward and \[\vec{B}\] points towards the north. The vector product \[\vec{A} \times \vec{B}\] is


The radius of a circle is stated as 2.12 cm. Its area should be written as


Add vectors \[\vec{A} , \vec{B} \text { and } \vec{C}\]  each having magnitude of 100 unit and inclined to the X-axis at angles 45°, 135° and 315° respectively.


Refer to figure (2 − E1). Find (a) the magnitude, (b) x and y component and (c) the angle with the X-axis of the resultant of \[\overrightarrow{OA}, \overrightarrow{BC} \text { and } \overrightarrow{DE}\].


Let A1 A2 A3 A4 A5 A6 A1 be a regular hexagon. Write the x-components of the vectors represented by the six sides taken in order. Use the fact the resultant of these six vectors is zero, to prove that
cos 0 + cos π/3 + cos 2π/3 + cos 3π/3 + cos 4π/3 + cos 5π/3 = 0.
Use the known cosine values to verify the result.


Let \[\vec{a} = 2 \vec{i} + 3 \vec{j} + 4 \vec{k} \text { and } \vec{b} = 3 \vec{i} + 4 \vec{j} + 5 \vec{k}\] Find the angle between them.


If  \[\vec{A} = 2 \vec{i} + 3 \vec{j} + 4 \vec{k} \text { and } \vec{B} = 4 \vec{i} + 3 \vec{j} + 2 \vec{k}\] find \[\vec{A} \times \vec{B}\].


If \[\vec{A} , \vec{B} , \vec{C}\] are mutually perpendicular, show that  \[\vec{C} \times \left( \vec{A} \times \vec{B} \right) = 0\] Is the converse true?


In a submarine equipped with sonar, the time delay between the generation of a pulse and its echo after reflection from an enemy submarine is observed to be 80 s. If the speed of sound in water is 1460 ms-1. What is the distance of an enemy submarine? 


Jupiter is at a distance of 824.7 million km from the Earth. Its angular diameter is measured to be 35.72˝. Calculate the diameter of Jupiter.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×