A small toy looks like a pipe and shoots a marble out each end. The toy is dropped out of a tree and fires halfway to be ground. One marble shoots directly up, the other directly down, Consider the vertical component of the acceleration ay of the marbles immediately after the marbles leave the toy, ignoring any air friction. (A) The upward-moving marble has ay 2 . (B) The upward-moving marhle has ay = -9.8 m/s 2 . (C) The upward-moving marble has ay -9.8 m/s 2 . (D) The downward-moving marble has a y -9.8 m/s 2 .

Question

A small toy looks like a pipe and shoots a marble out each end. The toy is dropped out of a tree and fires halfway to be ground. One marble shoots directly up, the other directly down, Consider the vertical component of the acceleration ay of the marbles immediately after the marbles leave the toy, ignoring any air friction. (A) The upward-moving marble has ay 2 . (B) The upward-moving marhle has ay = -9.8 m/s 2 . (C) The upward-moving marble has ay >-9.8 m/s 2 . (D) The downward-moving marble has a­ y > -9.8 m/s 2 .

Deepak Patra · Answer

The correct option is: (C) the upward-moving marble has a_y > -9.8 m / s².
Imagine that the marbles are shot by the pipe such that they move with constant velocities. This would ensure that the distance between both the marbles and the pipe remains the same with time and rule out the option (B).

Therefore, the distance between the marbles and the pipe increases only when the velocity of the marbles relative to the velocity of the pipe increases over time. Thus, a marble moving upward must have a positive acceleration with respect to the pipe. If the pipe falls vertically with acceleration -9.8 m /s2 , the marble moving upward should have acceleration greater than -9.8 m /s² such that the acceleration remains positive relative to the pipe.
Therefore, (C) is the correct option.

Oliver Wayne · Answer

@Deepak Patra Why can you make the assumption that the marbles move with constant velocities? Can you please provide a different explanation? Your explanation is good but I am not conceptually understanding it.

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