Question

During a lecture demonstration, a professor places two coins on the edge of a table. She then flicks one of the coins horizontally off the table, simultaneously nudging the other over the edge. Describe the subsequent motion of the two coins, in particular discussing whether they hit the floor at the same time.

Short answer

For the two coins to hit the floor at the same time, the vertical motions of these coins need to be compared. The coins start at the same point and the same height, and have no initial velocity along the vertical direction.Therefore, their vertical motions are similar, and they will hit the floor at the same time.

Step-by-step solution

Determine the velocity of the flicked coin

The flicked coin has an initial horizontal velocity while leaving the table. It is accelerated downwards due to the force of gravity.Since no force is acting along the horizontal direction, the accelerated downward motion caused the coin to travel a parabolic path, the trajectory of an object in projectile motion.

Determine the motion of the flicked coin

The horizontal velocity of the nudged coin is minimal. Therefore, this can be assumed to be zero. Only the force of gravity acts on it when it has zero horizontal velocity. The coin accelerates downhill and travels in a straight line.

Any motion in space can be broken down into separate motions along several axes. The constant-velocity horizontal motion and the accelerated downward motion are two independent motions within the instance of the flung coin.