Read each statement below carefully and state with reasons, if it is true or false:

**(a) **The magnitude of a vector is always a scalar

**(b)** Each component of a vector is always a scalar

**(c) **The total path length is always equal to the magnitude of the displacement vector of a particle

**(d)** The average speed of a particle (defined as total path length divided by the time taken to cover the path) is either greater or equal to the magnitude of the average velocity of the particle over the same interval of time

**(e) **Three vectors not lying in a plane can never add up to give a null vector.

Asked by Pragya Singh | 1 year ago | 125

**Right answer is (a) True**

**Explanation:-**

The magnitude of a vector is a number. So, it is a scalar.

**Right answer is (b) False**

**Explanation:-**

Each component of a vector is also a vector.

**Right answer is (c) False**

**Explanation:-**

The total path length is a scalar quantity, whereas displacement is a vector quantity. Hence, the total path length is always greater than the magnitude of displacement. It becomes equal to the magnitude of displacement only when a particle is moving in a straight line.

**Right answer is (d) True**

**Explanation:-**

It is because of the fact that the total path length is always greater than or equal to the magnitude of displacement of a particle.

**Right answer is (e) True**

**Explanation:-**

Three vectors, which do not lie in a plane, cannot be represented by the sides of a triangle taken in the same order.

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

\(\theta (t)=tan^{-1}(\dfrac{v_{0y-gt}}{v_{ox}})\)

**(b)** Shows that the projection angle θ_{0} for a projectile launched from the origin is given by

\(\theta_{0}=tan^{-1}(\dfrac{4h_{m}}{R})\)

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} ).

A bullet fired at an angle of 30° with the horizontal hits the ground 3.0 km away. By adjusting its angle of projection, can one hope to hit a target 5.0 km away? Assume the muzzle speed to be fixed, and neglect air resistance.

Can we associate a vector with

**(i)** a sphere

**(ii)** the length of a wire bent into a loop

**(iii)** a plane area

Clarify for the same.