# NCERT Class 11 Physics Solutions: Chapter 4 – Motion in a Plane Part 11

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**Question 4.26:**

A vector has magnitude and direction.

( I ) Does it have a location in space?

( ii )Can it vary with time?

( iii )Will two equal vectors a and b at different locations in space necessarily have identical physical effects?

Give examples in support of your answer.

**Answer:**

( I ) Does it have a location in space? **: No**

**Explanation:**

A vector has no definite locations in space. This is because a vector remains invariant when displaced in such a way that its magnitude and direction remain the same. However, a position vector has a definite location in space.

( ii ) Can it vary with time? : **Yes**

**Explanation:**

A vector can vary with time. For example, the displacement vector of a particle moving with a certain velocity varies with time.

( iii ) Will two equal vectors a and b at different locations in space necessarily have identical physical effects? **: No**

**Explanation:**

Two equal vectors located at different locations in space need not produce the same physical effect. For example, two equal forces acting on an object at different points can cause the body to rotate, but their combination cannot produce an equal turning effect.

**Question 4.27:**

A vector has both magnitude and direction.

( I ) Does it mean that anything that has magnitude and direction is necessarily a vector?

( ii ) The rotation of a body can be specified by the direction of the axis of rotation, and the angle of rotation about the axis. Does that make any rotation a vector?

**Answer:**

( I ) Does it mean that anything that has magnitude and direction is necessarily a vector: **No**

**Explanation:**

A physical quantity having both magnitude and direction need not be considered a vector. For example, despite having magnitude and direction, current is a scalar quantity. The essential requirement for a physical quantity to be considered a vector is that it should follow the law of vector addition.

( ii ) The rotation of a body can be specified by the direction of the axis of rotation, and the angle of rotation about the axis. Does that make any rotation a vector: **No**

**Explanation:**

Generally speaking, the rotation of a body about an axis is not a vector quantity as it does not follow the law of vector addition. However, a rotation by a certain small angle follows the law of vector addition and is therefore considered a vector.

**Question 4.28:**

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 the fixed, and neglect air resistance.

**Answer:** No

**Explanation:**

Range,

Angle of projection,

Acceleration due to gravity,

Horizontal range for the projection velocity, is given by the relation:

The maximum range is achieved by the bullet when it is fired at an angle of 45° with the horizontal, that is,

Hence, the bullet will not hit a target 5 km away.

**Question 4.30:**

A fighter plane flying horizontally at an altitude of 1.5 km with speed 720 km/h passes directly overhead an antiaircraft gun. At what angle from the vertical should the gun be fired for the shell with muzzle speed to hit the plane? At what minimum altitude should the pilot fly the plane to avoid being hit?

(Take)

**Answer:**

Height of the fighter plane

Speed of the fighter plane,

Let θ be the angle with the vertical so that the shell hits the plane.

The situation is shown in the given figure:

Muzzle velocity of the gun,

Time taken by the shell to hit the plane = t

Horizontal distance travelled by the shell

Distance travelled by the plane = t

The shell hits the plane. Hence, these two distances must be equal.

In order to avoid being hit by the shell, the pilot must fly the plane at an altitude (H) higher than the maximum height achieved by the shell.