State with reasons, whether the following algebraic operations with scalar and vector physical quantities are meaningful :
(a) Addition of any two scalars
(b) Adding a scalar to a vector which has the same dimensions
(c) Multiplying a vector by any scalar
(d) Multiplying any two scalars
(e) Adding any two vectors
(f) Addition of a vector component to the same vector.
The addition of two scalar quantities is meaningful only if they both represent the same physical quantity.
(b) Not Meaningful:
The addition of a vector quantity with a scalar quantity is not meaningful
A scalar can be multiplied with a vector. For example, force is multiplied with time to give impulse.
A scalar, irrespective of the physical quantity it represents, can be multiplied by another scalar having the same or different dimensions.
The addition of two vector quantities is meaningful only if they both represent the same physical quantity.
A component of a vector can be added to the same vector as they both have the same dimensions.Answered by Abhisek | 1 year ago
(a) Show that for a projectile the angle between the velocity and the x-axis as a function of time is given by
(b) Shows that the projection angle θ0 for a projectile launched from the origin is given by
where the symbols have their usual meaning
A cyclist is riding with a speed of 27 km/h. As he approaches a circular turn on the road of a radius of 80 m, he applies brakes and reduces his speed at the constant rate of 0.50 m/s every second. What is the magnitude and direction of the net acceleration of the cyclist on the circular turn?
A fighter plane flying horizontally at an altitude of 1.5 km with a speed of 720 km/h passes directly overhead an anti-aircraft gun. At what angle from the vertical should the gun be fired for the shell with muzzle speed 600 m s-1 to hit the plane? At what minimum altitude should the pilot fly the plane to avoid being hit? (Take g = 10 m s-2 ).