Apencil is rolled off a table of height 1.25 m. if it has a horizontal speed of 3.1 m/s, how long does it take the pencil to reach the ground? a. 0.51 s b. 1.12 s c. 0.40 s d. 2.48 s

The horizontal speed has no effect on how long it takes to reach the ground.
A bullet shot from a gun and a bullet dropped from the front end of the gun
at the same time as the shot both hit the ground at the same time.

The number that counts is the height from which it fell . . . the 1.25 m.

I'll use this very useful formula:

       Distance of free fall,
       starting from rest            = (1/2) · (gravity) · (time)²

                                  1.25 m  =  (1/2) · (9.8 m/s²) · (time)²

Divide each side
by   4.9 m/s²  :          1.25 m / 4.9 m/s²  =  time²

                                          0.2551 sec²  =  time²

Square root each side:       0.505 sec  =  time

It looks like the correct choice is approximately 'A'. (rounded)