A large, heavy box is sliding without friction down a smoot…

Physics Motion in a Plane General MCQ (Single Correct)

A large, heavy box is sliding without friction down a smooth plane of inclination . From a point P on the bottom of the box, a particle is projected inside the box. The initial speed of the particle with respect to the box is u, and the direction of projection makes an angle with the bottom as shown in figure.

Find the distance along the bottom of the box between the point of projection P and the point Q where the particle lands. (Assume that the particle does not hit any other surface of the box. Neglect air resistance)

If the horizontal displacement of the particle as seen by an observer on the ground is zero, find the speed of the box with respect to the ground at the instant when particle was projected.

Text Solution

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The correct answer is:

CHECK THE SOLUTION.

u is the relative velocity of the particle with respect to the box. Resolve u.

is the relative velocity of the particle with respect to the box in x-direction.
is the relative velocity of the particle with respect to the box in y-direction.
Since there is no velocity of the box in the y-direction, therefore this is the vertical velocity of the particle with respect to ground also.
Y - direction motion (Taking relative terms w.r.t. box)