A boy while moving in a straight line along the x -axis with velocity `u_(x)` attempts to throw a stone in the y-z plane with a velocity `u_(y)hat j+u_(z)hat k` .The horizontal range of the stone on the ground is given by:

A block is moving along y- axis with velocity vec(v)_(A)=4hat(j) on a plank relative to ground and the plank is moving along x- axis with velocity vec(v)_(P)=3hat(i) at any instant of time. The unit vector in dirction of fricition force acting on block at this moment is :-

An object A is kept fixed at the point x= 3 m and y = 1.25 m on a plank p raised above the ground . At time t = 0 the plank starts moving along the +x direction with an acceleration 1.5 m//s^(2) . At the same instant a stone is projected from the origin with a velocity vec(u) as shown . A stationary person on the ground observes the stone hitting the object during its downward motion at an angle 45(@) to the horizontal . All the motions are in the X -Y plane . Find vec(u) and the time after which the stone hits the object . Take g = 10 m//s

An object A is kept fixed at the point x= 3 m and y = 1.25 m on a plank p raised above the ground . At time t = 0 the plank starts moving along the +x direction with an acceleration 1.5 m//s^(2) . At the same instant a stone is projected from the origin with a velocity vec(u) as shown . A stationary person on the ground observes the stone hitting the object during its downward motion at an angle 45(@) to the horizontal . All the motions are in the X -Y plane . Find vec(u) and the time after which the stone hits the object . Take g = 10 m//s

A ball of mass '2m' moving with velocity u hat(i) collides with another ball of mass 'm' moving with velocity - 2 u hat(i) . After the collision, mass 2m moves with velocity (u)/(2) ( hat(i) - hat(j)) . Then the change in kinetic energy of the system ( both balls ) is

A point object infront of a plane mirror has velocity -2 hat i+ 3 hat j + 4 hat k and the mirror has velocity 3 hat i- 2 hat j+ 4 hat k . The x-axis is along the normal of the pane mirrro. Find the velocity of the image.

A small particle of mass m is projected at an angle theta with the x - axis with an initial velocity v_(0) in the x-y plane as shown in the figure . At a time t lt ( v_(0) sin theta)/(g) , the angular momentum of the particle is where hat (i) , hat (j) and hat(k) are unit vectors along x , y and z - axis respectively.

A helicopter is moving verticallly upwards with a velocity 5 ms^-1 . When the helicopter is at a height 10 m from ground, a stone is thrown with a velocity (3 hat i + 4 hat j) m s^-1 from the helicopter w.r.t. the man in it. Considering the point on ground vertically below the helicopter as the origin of coordinates, and the ground below as xy plane, find the coordinates of the point where the stone will fall, its distance from origin at the instant the stone strikes the ground, assuming helicopter moves upwards with constant velocity. .

A plane mirror is moving with velocity 4 (hat i) + 4 (hat j) + 8 (hat k) . A point object in front of the mirror moves with a velocity 3 (hat i) + 4 (hat j) + 5 (hat k) . Here, hat k is along the normal to the plane mirror and facing towards the object. The velocity of the image is

A plane mirror is moving with velocity 4 (hat i) + 4 (hat j) + 8 (hat k) . A point object in front of the mirror moves with a velocity 3 (hat i) + 4 (hat j) + 5 (hat k) . Here, hat k is along the normal to the plane mirror and facing towards the object. The velocity of the image is

The angles with a vector hat(i)+hat(j)+sqrt(2hat(k)) makes with X,Y and Z axes respectively are