Answer

Verified

47.4k+ views

**Hint:**The above problem is based on the vector subtraction and relative velocity concept. Airplane is heading towards north and wind is blowing towards east which means that velocity of airplane with respect to ground can be calculated by subtracting magnitude of velocity shown by speedometer and velocity of wind. Let’s get started with the vector subtraction to find out the speed of the plane with respect to round.

**Complete step by step solution:**

First let’s discuss vectors and relative velocity concepts in detail.

Vectors quantities are those which are characterised by both magnitude and direction. Vectors are represented by a line with an arrow head (which represents the direction of the vector).

Vector subtraction: The process of subtraction of one algebraic quantity from another is equivalent to adding the negative of the quantity to be subtracted.

The relative velocity is the velocity of an object or observer B in the rest frame of another object or observer A. Now, we calculate the velocity of the plane with respect to ground.

We will do vector subtraction by using the concept of Pythagoras theorem.

Velocity of an airplane will be denoted by $V_{ag}$ velocity of wind is $V_W$ and velocity of airplane $V_a$.

$

\Rightarrow {V^2}_{ag} = {V_a}^2 + {V_w}^2 \\

\Rightarrow {V_{ag}} = \sqrt {{V_a}^2 + {V_w}^2} \\

\Rightarrow {V_{ag}} = \sqrt {{{(240)}^2} + {{(100)}^2}} \\

$ (We have used the formula and substituted the value of velocities)

$

\Rightarrow {V_{ag}} = \sqrt {67600} \\

\Rightarrow {V_{ag}} = 260Km/hr \\

$ (We have done the square and added the value)

To find the angle of movement of airplane we will use

$

\Rightarrow \tan \theta = \dfrac{{{V_w}}}{{{V_a}}} \\

\Rightarrow \tan \theta = \dfrac{{100}}{{240}} \\

$ (We have use the tangent formula)

$

\Rightarrow \theta = {\tan ^{ - 1}}\dfrac{{100}}{{240}} \\

\Rightarrow \theta = 22.67 \\

\Rightarrow \theta = {23^0} \\

$

**Option (A) is correct.**

**Note:**Vector addition and subtraction can be done using two laws which are: parallelogram law of vector addition and triangle law of vector addition. In the triangle law of vector addition, the head of one vector is attached to the tail of another vector.

Recently Updated Pages

To get a maximum current in an external resistance class 1 physics JEE_Main

f a body travels with constant acceleration which of class 1 physics JEE_Main

A hollow sphere of mass M and radius R is rotating class 1 physics JEE_Main

If the beams of electrons and protons move parallel class 1 physics JEE_Main

Two radioactive nuclei P and Q in a given sample decay class 1 physics JEE_Main

silver wire has diameter 04mm and resistivity 16 times class 12 physics JEE_Main

Other Pages

Choose the correct statements A A dimensionally correct class 11 physics JEE_Main

Differentiate between homogeneous and heterogeneous class 12 chemistry JEE_Main

If a wire of resistance R is stretched to double of class 12 physics JEE_Main

The force of interaction of two dipoles if the two class 12 physics JEE_Main

The resultant of vec A and vec B is perpendicular to class 11 physics JEE_Main

Electric field due to uniformly charged sphere class 12 physics JEE_Main