Physics Motion in Plane

A swimmer wants to cross a river from point A to point B. Line AB makes an angle of 30° with the flow of river. Magnitude of velocity of the swimmer is same as that of the river. The angle with the line AB should be _____°, so that the swimmer reaches point B.

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Assertion A: If A, B, C, D are four points on a semi-circular arc with centre at 'O' such that |AB| = |BC| = |CD|, then AB + AC + AD = 4AO + OB + OC
Reason R: Polygon law of vector addition yields AB + BC + CD = AD = 2AO

In the light of the above statements, choose the most appropriate answer from the options given below:

Match List I with List II.

Choose the correct answer from the options given below :

A planet revolving in elliptical orbit has:

(A) a constant velocity of revolution.

(B) has the least velocity when it is nearest to the sun.

(C) its areal velocity is directly proportional to its velocity.

(D) areal velocity in inversely proportional to its velocity.

(E) To follow a trajectory such that the areal velocity is constant.

Choose the correct answer from the options given below

The trajectory of a projectile in an vertical plane is y = αx - βx², where α and β are constants and x & y are respectively the horizontal and vertical distances of the projectile from the point of projection. The angle of projection θ and the maximum height attained H are respectively given by:

A particle is moving with uniform speed along the circumference of a circle of radius of radius R under the action of a central fictitious force F which is inversely proportional to R³. Its time period of revolution will be given by

If $\overrightarrow{P}*\overrightarrow{Q}=\overrightarrow{Q}*\overrightarrow{P},$ the angle between $\overrightarrow{P}and\overrightarrow{Q}is\theta \left(0°<\theta <360°\right).$ The value of 'θ' will be………

Varying velocity and varying acceleration

If the initial velocity in horizontal direction of a projectile is unit vector $\widehat{i}$  and the equation of trajectory is y = 5x(1 – x). The y component vector of the initial velocity is ________ $\widehat{j}$ .