← Projectiles: two independent motions

Faster launch, same flight time

Two marbles roll off the same table at the same instant. One leaves the edge at 2 m/s. The other leaves at twice that speed. Which marble hits the floor first?

Both marbles leave the edge moving only sideways, so each starts with zero vertical velocity. From that moment, each marble's vertical motion is free fall.

The flight ends when a marble reaches the floor. Only the vertical motion carries a marble downward.

tablethe 2 m/s marblethe 4 m/s marble
Strobe view of the two flights. At every tick the two marbles are level, and both reach the floor on the same tick.

Both marbles start with zero vertical velocity, and both fall from the same height with the same free-fall acceleration. So their vertical motions are identical from edge to floor.

The launch speed is horizontal, and the horizontal motion cannot touch the fall: because perpendicular components of motion do not affect each other, each direction can be analyzed as its own one-dimensional motion.

So the two marbles are level with each other at every moment of the fall, and they land at the same instant.

The launch height sets the flight time. The launch speed does not change it.

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?

Two toy cars run off the end of the same counter, one slow and one fast, and both reach the floor together. Why does the launch speed leave the flight time unchanged?

Two pucks slide off the same counter at the same instant, one at 1.0 m/s and one at 3.0 m/s. Which puck hits the floor first?

Both pucks leave the counter with zero vertical velocity.

Both fall from the same height with the same free-fall acceleration.

The launch speeds are horizontal, and they are perpendicular to the fall, so they cannot change it.

Neither: both pucks land at the same time.

Two identical darts are launched horizontally from the same ledge at the same instant, one at 5 m/s and one at 10 m/s. Ruth says the 10 m/s dart will take longer to reach the ground. Is she correct?

Your turn

Two drones fly level at the same height, one faster than the other. Each releases an identical package at the same instant. Which statement about the two packages is true?

A puck leaves a counter top at 3 m/s and lands on the floor. The test is repeated with the puck leaving at 9 m/s. Which quantity is unchanged between the two flights?

Two stones leave a sea wall horizontally at the same instant, one at 4 m/s and one at 12 m/s. After 0.5 s, both are still in the air. Which statement compares their heights at that moment?