Motion in a Plane

A bullet is fired from a gun at the speed of 280 m s-1 in the direction 30 above the horizontal. The maximum height attained by the bullet is (g = 9.8 m s-2, 30 = 0.5 ) :-

1. 2000 m
2. 1000 m
3. 3000 m
4. 2800 m

A ball is projected with a velocity, 10 m s-1, at an angle of 60 with the vertical direction. Its speed at the highest point of its trajectory will be

1. Zero
2. 5 3 m s-1
3. 5 m s-1
4. 10 m s-1

A cricket ball is thrown by a player at a speed of 20 m/s in a direction 30 above the horizontal. The maximum height attained by the ball during its motion is (g = 10 m/s2)

1. 25 m
2. 5 m
3. 10 m
4. 20 m

A particle moving in a circle of radius R with a uniform speed takes a time T to complete one revolution. If this particle were projected with the same speed at an angle ' ' to the horizontal, the maximum height attained by it equals 4R. The angle of projection, , is then given by :

1. = -1 ( 2gT2 2 R )1/2
2. = -1 ( gT2 2 R )1/2
3. = -1 ( 2 RgT2 )1/2
4. = -1 ( 2 RgT2 )1/2

A car starts from rest and accelerates at 5 m/s2. At t = 4 s, a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at t = 6 s? (Take g = 10 m/s2)

1. 20 2 m/s, 10 m/s2
2. 20 m/s, 5 m/s2
3. 20 m/s, 0
4. 20 2 m/s, 0

A projectile is fired from the surface of the earth with a velocity of 5 m s-1 and angle with the horizontal. Another projectile fired from another planet with a velocity of 3 m s-1 at the same angle follows a trajectory which is identical with the trajectory of the projectile fired from the earth. The value of the acceleration due to gravity on the planet (in m s-2) is (Given g = 9.8 m s-2)

1. 3.5
2. 5.9
3. 16.3
4. 110.8

The velocity of a projectile at the initial point A is (2 i + 3 j) m/s. Its velocity (in m/s) at point B is [figure]

1. 2 i - 3 j
2. 2 i + 3 j
3. -2 i - 3 j
4. -2 i + 3 j

The horizontal range and the maximum height of a projectile are equal. The angle of projection of the projectile is

1. = -1 ( 14 )
2. = -1(4)
3. = -1(2)
4. = 45

A projectile is fired at an angle of 45 with the horizontal. Elevation angle of the projectile at its highest point as seen from the point of projection, is

1. 45
2. 60
3. -1 ( 12 )
4. -1 ( 32 )

A missile is fired for maximum range with an initial velocity of 20 m/s. If g = 10 m/s2, the range of the missile is

1. 40 m
2. 50 m
3. 60 m
4. 20 m

The speed of a projectile at its maximum height is half of its initial speed. The angle of projection is

1. 60
2. 15
3. 30
4. 45

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

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.

A particle A is dropped from a height and another particle B is projected in horizontal direction with speed of 5 m/sec from the same height then correct statement is

1. particle A will reach at ground first with respect to particle B
2. particle B will reach at ground first with respect to particle A
3. both particles will reach at ground simultaneously
4. both particles will reach at ground with same speed.

A particle is projected making an angle of 45 with horizontal having kinetic energy K. The kinetic energy at highest point will be

1. K 2
2. K2
3. 2K
4. K

Two projectiles of same mass and with same velocity are thrown at an angle 60 and 30 with the horizontal, then which will remain same

1. time of flight
2. range of projectile
3. maximum height acquired
4. all of them