Final answer:
The vertical velocity (vf) when an object hits the ground can be determined using kinematic equations with initial vertical velocity, gravity's acceleration, and time of fall. If the object has no initial vertical velocity, the formula simplifies to v = at. For an object falling from rest, time of fall can be computed as t = √(2y/g) where y is the vertical displacement.
Step-by-step explanation:
To find the vertical velocity (vf) of a cylinder (or any object) when it hits the ground, we can use kinematic equations that relate initial velocity, acceleration due to gravity, and the vertical displacement of the object. Since the problem specifies that the initial vertical velocity is zero relative to the ground and neglects any horizontal motion or acceleration, the final vertical velocity will be directed downwards and can be calculated with the formula v = v₁ + at, where v₁ is the initial velocity, a is the acceleration due to gravity, and t is the time the object is in free-fall.
When an object falls from rest, v₁ is zero and hence the formula simplifies to v = at. The acceleration due to gravity (a) is commonly approximated as 9.81 m/s², directed downward (hence, it's negative when the upward direction is positive). To solve for t, we could use the formula t = √(2y/g), where y is the vertical displacement.
For a given example where the object falls a height of 20.0 m, y would be -20.0 m because it is directed downwards. Substituting the known values into the equation provides us with the final vertical velocity (vf). It's crucial to note that if the object starts with an initial vertical velocity that is not zero, this would also be taken into account in the calculation by including v₁ in our formula.