Explanation:
To find the marble's speed when it hits the floor, we can use the principle of conservation of energy. The potential energy the marble possesses at the top (due to its height above the ground) is converted into kinetic energy as it falls.
The potential energy (PE) of the marble at the top of the table is given by:
\[PE = mgh\]
where:
- \(m\) is the mass of the marble,
- \(g\) is the acceleration due to gravity (9.81)
At the bottom, the marble's kinetic energy (KE) is given by:
KE : 1/2mv^2
where:
- v is the speed of the marble.
Since energy is conserved, we can equate the potential energy at the top to the kinetic energy at the bottom:
mgh=1/2mv^2
Canceling out \(m\) from both sides and solving for \(v\), we get:
\v= square root 2gh
Now we can plug in the values:
v= square root, 2x9.81x1
speed = 4.43 m/s
