Question

all formula of chapter motion in a plane class 11

Answer 1

Answer:

Explanation:

Addition of Vectors :-

(i) Only vectors of same nature can be added.

(ii) The addition of two vector A and B is resultant R

Addition of Vectors

Where Θ is the angle between vector A and vector B, And β is the angle which R makes with the direction of A.

(iii) Vector addition is commutative A + B = B+A

(iv) Vector addition is associative,A+ (B +C ) = (A +B )+C

(v) R is maximum if Θ = 0 and minimum if Θ = 180 + 0 .

Subtraction of two vectors :-

(i) Only vector of same nature can be subtracted.

(ii) Subtraction of B from A = vector addition of A and (-B),

Subtraction of two vectors

Where Θ is the angle between A and B and β is the angle which R makes with the direction of A.

(iii) Vector addition is commutative A + B ≠ B+A

(iv) Vector addition is associative,A+ (B +C ) ≠ (A +B )+C

Rectangular components of a vector in a plane :-

If A makes an angle Θ with x-axis and Ax and By be the rectangular components of A along X-axis and Y- axis respectively.

Then A= A x + By= y

Here A x =A CosΘ and B y = ASinΘ

Dot product or scalar product : -

The dot product of two vectors A and B, represented by . is a scalar , which is equal to the product of the magnitudes of A and B and the Cosine of the smaller angle between them. If Θ is the smaller angle between A and B, then AB= AB

Dot product or scalar product

Cross or Vector product :-

The cross product of two vectors and , represented by x is a vector , which is equal to the product of the magnitudes of A and B and the sine of the smaller angle between them. If Θ is the smaller angle between A and B, then = AB Sinθ

Cross or Vector product

Projectile motion : -

Projectile is the name given to anybody which once thrown in to space with some initial velocity, moves thereafter under the influence of gravity alone without being propelled by any engine or fuel. The path followed by a projectile is called its trajectory.

Answer 2

FORMULAS FOR MOTION IN A PLANE :

• For class 11-12 standards, we will have to consider CIRCULAR AND PARABOLIC Motions under this topic.

FOR CIRCULAR MOTION:

$1) \:\theta=\omega t+\dfrac{1}{2} \alpha t^{2}$

$2) \:\omega^{2}=(\omega_{0})^{2} +2\alpha \theta$

$3)\: \omega=\omega_{0} +\alpha t$

$\omega$ is angular velocity, $\theta$ is angular displacement and $\alpha$ is angular acceleration and "t" is time.

FOR PARABOLIC PROJECTILE:

$1)\: Range(R)=\dfrac{u^{2}\sin(2\theta) }{g}$

$2)\: Max Height = \dfrac{u^{2}\sin^{2}(\theta) }{2g}$

$3)\: y=x\tan(\theta)-\dfrac{gx^{2} }{2u^{2}\cos^{2}(\theta) }$

"u" is initial velocity of projection, $\theta$ is angle of projection, "g" is gravity .

Hope It Helps