Motion in a Plane

Two projectiles are fired from ground with same initial speeds from same point at angles (45 + ) and (45 - ) with horizontal direction. The ratio of their times of flights is

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

A helicopter flying horizontally with a speed of 360 km/h at an altitude of 2 km, drops an object at an instant. The object hits the ground at a point O, 20 s after it is dropped. Displacement of 'O' from the position of helicopter where the object was released is : (use acceleration due to gravity g = 10 m/s2 and neglect air resistance)

1. 7.2 km
2. 2 5 km
3. 2 2 km
4. 4 km

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 .