Motion in a Plane

Two balls with same mass and initial velocity, are projected at different angles in such a way that maximum height reached by first ball is 8 times higher than that of the second ball. T1 and T2 are the total flying times of first and second ball, respectively, then the ratio of T1 and T2 is

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

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