← Projectiles: two independent motions

Dropped and launched land together

What is true of a projectile's horizontal and vertical motions?

At the same instant, one coin is flicked hard off a table edge and a second coin is nudged straight off. The flicked coin flies far out into the room. The nudged coin drops at the table's foot. Which coin hits the floor first?

The flicked coin travels a far longer path. Before any reasoning, commit to a prediction on a fresh pair.

A quarter is dropped from a dresser top at the instant another quarter is launched horizontally from the same height. Which quarter lands first?

Now take the coin question one direction at a time. Both coins leave the table at the same height, at the same instant.

Take the vertical direction only. Each coin's vertical motion is free fall.

The flicked coin's sideways motion cannot change its fall: because perpendicular components of motion do not affect each other, each direction can be analyzed as its own one-dimensional motion.

shelffloorthe dropped ballthe launched ball
Same ticks, same heights: the sideways motion never changes the fall.

So the two falls are identical: the same height, the same free fall, the same fall time.

The coins hit the floor together. A ball dropped from rest and a ball launched horizontally from the same height at the same moment hit the ground together.

A marble is dropped from a deck rail as an identical marble is launched horizontally from the same rail. Why do they land together?

The flicked coin does cover more ground, but its extra path is sideways path. A longer path does not mean a longer time.

A ball bearing is dropped from a shelf at the instant an identical bearing is launched horizontally from the same shelf. The launched bearing lands 2 m out from the shelf. Which bearing lands first?

Both bearings start falling from the same height at the same instant.

Each bearing's vertical motion is free fall, and the launched bearing's sideways motion does not change its fall.

So both falls take the same time.

Neither: they land together.

Two pebbles leave a wall top at the same instant, one dropped and one launched horizontally. Where is the dropped pebble when the launched pebble lands?

Your turn

An arrow is fired horizontally from shoulder height at the instant a second arrow is dropped from the same height. Which arrow reaches the ground first?

A bolt slips off a girder as an identical bolt is launched horizontally from the same height at that instant. Why do they hit the ground at the same time?

A launched ball travels a much longer path than a ball dropped from the same height at the same moment. Which statement about their flight times is true?