Motion in a Plane

Two identical bodies, projected with the same speed at two different angles cover the same horizontal range R. If the time of flight of these bodies are 5 s and 10 s, respectively, then the value of R is m. (Take g=10 m/s2)

1. 250
2. 25
3. 500
4. 125

The two projectiles are projected with the same initial velocities at the 15° and 30° with respect to the horizontal. The ratio of their ranges is 1:x. The value of x is

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

If x and y coordinates of a projectile as a function of time (t) are given as 24t and 43.6t-4.9t2, respectively, then the angle (in degrees) made by the projectile with horizontal when t=2 s is .

1. 60
2. 45
3. 30
4. 75

A gun mounted on the ground fires bullets in all directions with same speed. The farthest distance the bullets could reach is 6.4 m. The speed of the bullets from the gun is m/s. (take g=10 m/s2)

The velocity of a particle is given as v=-x i+2y j-z k m/s. The magnitude of acceleration at point (1, 2, 4) is m/s2.

1. 6
2. 9
3. 33
4. 0

A boy throws a ball into air at 45 from the horizontal to land it on a roof of a building of height H. If the ball attains maximum height in 2 s and lands on the building in 3 s after launch, then value of H is m. (g = 10 m/s2)

1. 20
2. 25
3. 10
4. 15

An object is projected with kinetic energy K from a point A at an angle 60 with the horizontal. The ratio of the difference in kinetic energies at points B and C to that at point A (see figure), in the absence of air friction is : [figure]

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

A projectile is thrown upward at an angle 60 with the horizontal. The speed of the projectile is 20 m/s when its direction of motion is 45 with the horizontal. The initial speed of the projectile is m/s.

1. 20 3
2. 20 2
3. 40
4. 40 2

A river of width 200 m is flowing from west to east with a speed of 18 km/h. A boat, moving with speed of 36 km/h in still water, is made to travel one-round trip (bank to bank of the river). Minimum time taken by the boat for this journey and also the displacement along the river bank are and respectively.

1. 20 s and 100 m
2. 40 s and 100 m
3. 40 s and 200 m
4. 40 s and 0 m

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

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 ]

If a and b make an angle -1 ( 59 ) with each other, then | a + b| = 2| a - b| for | a| = n| b|. The integer value of n is .

The resultant of two vectors A and B is perpendicular to A and its magnitude is half that of B. The angle between vectors A and B is .

A clock has 75 cm, 60 cm long second hand and minute hand respectively. In 30 minutes duration the tip of second hand will travel x distance more than the tip of minute hand. The value of x in meter is nearly (Take = 3.14) :

1. 118.9
2. 140.5
3. 139.4
4. 220.0

Three vectors OP, OQ and OR each of magnitude A are acting as shown in figure. The resultant of the three vectors is A x. The value of x is . [figure]

The angle of projection for a projectile to have same horizontal range and maximum height is :

1. -1 ( 12 )
2. -1(2)
3. -1 ( 14 )
4. -1(4)

A body of mass M thrown horizontally with velocity v from the top of the tower of height H touches the ground at a distance of 100 m from the foot of the tower. A body of mass 2 M thrown at a velocity v2 from the top of the tower of height 4H will touch the ground at a distance of m.

For three vectors A = (-x i - 6 j - 2 k), B = (- i + 4 j + 3 k) and C = (-8 i - j + 3 k), if A ( B C) = 0, then value of x is .

The angle between vector Q and the resultant of (2 Q + 2 P) and (2 Q - 2 P) is :

1. -1(P/Q)
2. 0
3. -1 (2 Q - 2 P)2 Q + 2 P
4. -1(2Q/P)