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Let A be a vector such that:-                  Then the magnitude of vector A is given by   :             Now let us assume that the angle made between vector A and x-axis is . Then we have:-                                                                                   Similarly, let B be a vector such that:-        The magnitude of vector B is     :                        Let  be the angle...
(b)     The maximum height is given by   :                                                                        And,     the horizontal range is given by  :                                                                       Dividing both, we get :                                                                      Hence                                                           
Using the equation of motion in both horizontal and vertical direction.                                                   and         Now,                                                                                   or                                                              Thus,                                              
Speed of cycle =   27 Km/h  =  7.5 m/s The situation is shown in figure :-                                 The centripetal acceleration is given by :                                                                                                                                                     And the tangential acceleration is given as  . So, the net acceleration becomes :                  ...
According to the question the situation is shown below:-                                               Now,  The horizontal distance travelled by the shell  =  Distance travelled by plane or                                          or                                               or                                                              So,                                                 ...
The range of bullet is given to be:-       R = 3 Km.                                                            or                                                        or                                                         Now, we will find the maximum range (maximum range occurs when the angle of projection is 450).                                                              or         ...
No,vector cannot be associated with sphere as direction cannot be associated with sphere any how.
(b) The plane area can be expressed in vector form as direction can be associated as pointing outward or inward (normal to the plane) of the area.
No, the length of a wire bent into a loop cannot be expressed in vector form as we have no direction associated with it.
The main condition for a physical quantity to be a vector is that it should the law of vector addition. Also, the vector has both direction and, magnitude but these are not sufficient condition. For e.g. current has both magnitude and direction but is a scalar quantity as it doesn't follow the law of vector addition. Rotation is not a vector on a large basis, as it is measured by an angle which...
No, a vector doesn't have a definite location as a vector can be shifted in a plane by maintaining its magnitude and direction. Vector can change with time for e.g. displacement vector. No, two equal vectors at a different location may not have identical physical effects. For e.g., two equal force vectors at a different location may have different torque but when they are applied together the...
The given situation is shown in the figure:-                                For finding the speed of aircraft we just need to find the distance AC as we are given t = 10 sec. Consider  ABD,                                                                                       or                                        or                                                   or                       ...
(a) False:-  For e.g. energy is a scalar quantity but is not conserved in inelastic collisions. (b) False:-  For example temperature can take negative values in degree Celsius. (c) False:- Since speed is a scalar quantity but has dimensions. (d) False:-  Gravitational potential varies in space from point to point. (e) True:- Since it doesn't have direction. 
(a) False:-  Since it is arbitrary motion so the following relation cannot hold all the arbitrary relations. (b) True:-   This is true as this relation relates displacement with time correctly. (c) False: -  The given equation is valid only in case of uniform acceleration motion. (d) False:-   The given equation is valid only in case of uniform acceleration motion. But this is arbitrary motion...
The velocity of particle is given by :                                                              Put  t = 2 sec,  So velocity becomes :                                                                 or                                                            Now,  the magnitude of velocity gives :                                                                                            ...
We are given the velocity of the particle as  . And the acceleration is given as :                                                             So, the velocity due to acceleration will be :                                                                So,                                                          By integrating both sides, or                                                     ...
Put value of time   t  = 2   in the velocity vector as given below :                                                                                                   or                                                                                              or                                                                                                    Thus magnitude of velocity is...
(a)  We are given the position vector     The velocity vector is given by:-     or     Now for acceleration :                     
True:-  In a uniform circular motion, acceleration is radially outward all along the circular path. So in 1 complete revolution, all the vectors are cancelled and the null vector is obtained. 
True:- Because particle moves on the circumference of the circle, thus at any its direction should be tangential in order to move in a circular orbit.
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