Answer:
Approximately
(assuming that air resistance on the marble is negligible, and that
.)
Step-by-step explanation:
Start by finding the duration
of the flight of the marble.
If the air resistance on the marble is negligible, the marble will accelerate downward at a constant
.
Let
denote the initial vertical velocity of the marble. Let
denote the vertical displacement (change in height) of the marble.
.
Since the marble was launched horizontally,
. This equation becomes:
.
The marble was launched from a height of
above the floor. When the marble lands, it would be
below where it was launched. Hence, the vertical displacement of the flight will be
.
Solve the equation for
:
.
.
In other words, the marble was in the air for approximately
before landing.
Also because the air resistance on the marble is negligible, the horizontal velocity of the marble will be constant during the entire flight.
The marble achieved a horizontal displacement
of
in that flight of approximately
. Hence, the (initial) horizontal velocity
of the marble will be:
.
Combine both the initial horizontal and vertical velocity of the marble to find the initial speed
:
.