Motion in a Plane

A vector has magnitude same as that of A=3 i+4 j and is parallel to B=4 i+3 j. The x and y components of this vector in first quadrant are x and 3 respectively where x= .

A ball rolls off the top of a stairway with horizontal velocity u. The steps are 0.1 m high and 0.1 m wide. The minimum velocity u with which that ball just hits the step 5 of the stairway will be x ms-1 where x= [use g=10 m/s2].

A particle is moving in a circle of radius 50 cm in such a way that at any instant the normal and tangential components of its acceleration are equal. If its speed at t=0 is 4 m/s, the time taken to complete the first revolution will be 1 [1-e-2 ]s, where = .

Position of an ant (S in metres) moving in Y-Z plane is given by S=2t2 j+5 k (where t is in second). The magnitude and direction of velocity of the ant at t=1 s will be :

1. 16 m/s in y-direction
2. 4 m/s in x-direction
3. 9 m/s in z-direction
4. 4 m/s in y-direction

A particle starts from origin at t = 0 with a velocity 5 i m/s and moves in x-y plane under action of a force which produces a constant acceleration of (3 i + 2 j) m/s2. If the x-coordinate of the particle at that instant is 84 m, then the speed of the particle at this time is m/s. The value of is .