Motion in a Plane

If L and P represent the angular momentum and linear momentum respectively of a particle of mass 'm' having position vector as r = a( i t + j t). The direction of force is

1. Opposite to the direction of L
2. Opposite to the direction of L P
3. Opposite to the direction of r
4. Opposite to the direction of P

The angle of projection of a particle is measured from the vertical axis as and the maximum height reached by the particle is hm. Here hm as function of can be presented as

1. [figure]
2. [figure]
3. [figure]
4. [figure]

A particle is projected with velocity u so that its horizontal range is three times the maximum height attained by it. The horizontal range of the projectile is given as nu225g, where value of n is: (Given, 'g' is the acceleration due to gravity.)

1. 6
2. 12
3. 18
4. 24

A river is flowing from west to east direction with speed of 9 km h-1. If a boat capable of moving at a maximum speed of 27 km h-1 in still water, crosses the river in half a minute, while moving with maximum speed at an angle of 150 to direction of river flow, then the width of the river is :

1. 112.5 m
2. 75 m
3. 300 m
4. 112.5 3 m

Two projectiles are fired with same initial speed from same point on ground at angles of (45 - ) and (45 + ), respectively, with the horizontal direction. The ratio of their maximum heights attained is :

1. 1+ 1-
2. 1+ 2 1- 2
3. 1- 1+
4. 1- 2 1+ 2

The maximum speed of a boat in still water is 27 km/h. Now this boat is moving downstream in a river flowing at 9 km/h. A man in the boat throws a ball vertically upwards with speed of 10 m/s. Range of the ball as observed by an observer at rest on the bank is cm. (Take g = 10 m/s2)

The position vector of a moving body at any instant of time is given as r= (5t2 i-5t j ) m. The magnitude and direction of velocity at t=2 s is,

1. 5 17 m/s, making an angle of -14 with -ve Y axis
2. 5 15 m/s, making an angle of -14 with +ve X axis
3. 5 17 m/s, making an angle of -14 with +ve X axis
4. 5 15 m/s, making an angle of -14 with -ve Y axis

Two particles are located at equal distance from origin. The position vectors of those are represented by A=2 i+3n j+2 k and B=2 i-2 j+4p k, respectively. If both the vectors are at right angle to each other, the value of n-1 is .

A ball having kinetic energy KE, is projected at an angle of 60 from the horizontal. What will be the kinetic energy of ball at the highest point of its flight?

1. (KE)2
2. (KE)8
3. (KE)4
4. (KE)16

A particle is projected at an angle of 30 from horizontal at a speed of 60 m/s. The height traversed by the particle in the first second is h0 and height traversed in the last second, before it reaches the maximum height, is h1. The ratio h0:h1 is . [Take, g=10 m/s2 ]