Apencil rolls horizontally of a 1 meter high desk and lands .25 meters from the base of the desk. how fast was the pencil rolling when it left the desk?

0.55 m/s

Explanation:

This situation is related to projectile motion (also called parabolic motion), where the main equations are as follows:

(1)

(2)

Where:

is the horizontal displacement of the pencil

is the pencil's initial velocity

since we are told the pencil rolls horizontally before falling

is the time since the pencil falls until it hits the ground

 is the initial height of the pencil

 is the final height of the pencil (when it finally hits the ground)

 is the acceleration due gravity, always acting vertically downwards

Begining with (1):

(3)

(4)

Finding from (2):

(5)

(6)

Substituting (6) in (4):

(7)

Isolating :

(8)

(9)

Finally: