Motion in a Plane · Question 1

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