Motion in a Plane · Question 32

Six vectors, a through f have the magnitudes and directions indicated in the figure. Which of the following statements is true? [figure]

1. b + c = f
2. d + c = f
3. d + e = f
4. b + e = f

A particle of mass m is projected with velocity v making an angle of 45 with the horizontal. When the particle lands on the level ground the magnitude of the change in its momentum will be :

1. mv 2
2. zero
3. 2mv
4. mv/ 2

A and B are two vectors and θ is the angle between them. If | A B| = 3 ( A B), the value of θ is

1. 45
2. 30
3. 90
4. 60

A particle starting from the origin (0, 0) moves in a straight line in the (x, y) plane. Its coordinates at a later time are ( 3, 3 ). The path of the particle makes with the x-axis an angle of

1. 45
2. 60
3. 0
4. 30

A car runs at a constant speed on a circular track of radius 100 m, taking 62.8 seconds for every circular lap. The average velocity and average speed for each circular lap respectively is

1. 10 m/s, 0
2. 0, 0
3. 0, 10 m/s
4. 10 m/s, 10 m/s.

For angles of projection of a projectile at angle (45 - ) and (45 + ), the horizontal range described by the projectile are in the ratio of

1. 2 : 1
2. 1 : 1
3. 2 : 3
4. 1 : 2.

The vectors A and B are such that | A + B| = | A - B|. The angle between the two vectors is

1. 45
2. 90
3. 60
4. 75

Two boys are standing at the ends A and B of a ground where AB = a. The boy at B starts running in a direction perpendicular to AB with velocity v1. The boy at A starts running simultaneously with velocity v and catches the other in a time t, where t is

1. a v2 + v12
2. av + v1
3. av - v1
4. a2v2 - v12

A stone tied to the end of a string of 1 m long is whirled in a horizontal circle with a constant speed. If the stone makes 22 revolutions in 44 seconds, what is the magnitude and direction of acceleration of the stone?

1. 2 m s-2 and direction along the radius towards the centre
2. 2 m s-2 and direction along the radius away from the centre
3. 2 m s-2 and direction along the tangent to the circle
4. 2/4 m s-2 and direction along the radius towards the centre.

If the angle between the vectors A and B is , the value of the product ( B A ) A is equal to

1. BA2
2. BA2
3. BA2
4. zero.