← Projectiles: two independent motions

Faster launch, longer reach

Two balls roll off the same workbench at the same instant, one at 1.5 m/s and one at 4 m/s. Which ball lands first?

The two marbles from the last lesson landed at the same instant. They did not land in the same place. The faster marble hit the floor well out from the table's edge. Why does a faster launch reach farther?

The last lesson settled the time: the two marbles were in the air for exactly the same time. During that time, each marble kept its own horizontal velocity, because a projectile's horizontal velocity never changes once it is airborne.

The landing spot is set by the horizontal motion alone. A marble lands as far out as its horizontal velocity carries it during the flight.

tableslower marblefaster marble
Same flight time for both marbles. The faster marble covers more floor in each tick, so it lands farther from the table's base.

Both marbles fly for the same time. The faster marble moves farther sideways in every second of that time.

So at the same launch height, a faster launch lands farther from the base. The flight time has not changed; only the sideways distance covered in that time has.

Two balls roll off the same shelf at the same instant, one at 2 m/s and one at 5 m/s. Which ball lands farther from the shelf's base?

Two toy trucks run off the end of a bench together, and the faster truck lands farther out. Why does it land farther out?

Two identical coins are flicked horizontally off the same desk at the same instant, one at 1 m/s and one at 2 m/s. Which coin lands farther from the desk?

Both coins fall from the same height, so both flights last the same time.

During that time, the 2 m/s coin moves farther sideways in every second than the 1 m/s coin.

The 2 m/s coin lands farther from the desk.

Two identical pucks slide off a workbench at the same instant, one slow and one fast. Stefan says that since both pucks are in the air for the same time, the faster puck lands farther from the bench. Is he correct?

Your turn

A garden hose is held level at waist height. The tap is opened wider, so the water leaves the nozzle faster. What happens to where the water lands?

A coin is flicked horizontally off the same ledge twice, the second time faster. Which statement about the second flight is true?

Two identical balls roll off a dock at the same instant and land in the water together, one splashing 1 m out and the other 3 m out. Which ball left the dock faster?