Final answer:
To find the time of the fall and the height from which a pencil was dropped to reach a velocity of 50 m/s, the equations of motion with constant acceleration are used. The time of the fall is approximately 5.1 seconds, and the height dropped is approximately 128.0 meters.
Step-by-step explanation:
To determine the time of the fall when a pencil is dropped from rest and hits the ground traveling with a velocity of 50 m/s, we can use the kinematic equation for uniformly accelerated motion:
v = u + at
Here, v is the final velocity (50 m/s), u is the initial velocity (0 m/s), a is the acceleration due to gravity (9.81 m/s2), and t is the time in seconds. Rearranging the equation for time, we get:
t = (v - u) / a
Inserting the values:
t = (50 m/s) / (9.81 m/s2) ≈ 5.1 seconds
To find the height from which the pencil was dropped, we use the equation:
h = ut + ½at2
Again, with u = 0, the height h becomes:
h = ½ * 9.81 m/s2 * (5.1 s)2 ≈ 128.0 meters
Therefore, the time of the fall is approximately 5.1 seconds, and the height dropped is approximately 128.0 meters.