Albert Jr. takes his new skateboard out to the top of the loading ramp. The ramp is 30 m long and sloped at an angle of 15 degrees relative to the horizontal. Assuming he starts from rest, and neglecting friction, about how fast is Albert Jr. going at the bottom of the ramp?

vf = 12.343 m/s

Explanation:

Given:

- The Length of the ramp s = 30 m

- The angle of the ramp θ = 15 degrees

- Initial velocity at the top of ramp vi = 0

- Neglect Friction

Find:

How fast is Albert Jr. going at the bottom of the ramp?

Solution:

- We can use conservation of energy for the skateboard at top and bottom of the ramp.

                                ΔK.E = ΔP.E

Where, ΔK.E : Change in kinetic energy

            ΔP.E : Change in gravitational potential energy

                                0.5*m*(vf^2 - vi^2) = m*g*Δh

Where, m: The mass of the object

            Δh: Change in elevation from top to bottom

                                Δh = s*sin(θ)

- Substitute and simplify:

                                 0.5*(vf^2 - vi^2) = g*s*sin(θ)

                                 vf^2 = 2*g*s*sin(θ)

                                 vf = √(2*g*s*sin(θ)) = √(2*9.81*30*sin(15))

                                 vf = 12.343 m/s

- The velocity at the bottom of ramp would be 12.343 m/s

this is an example of "committed" time.

committed time, as contracted time, takes need over essential and available time since it is seen as profitable work. it alludes to the time allotted to keep up a home and family. at the point when a man is commuting using committed time this individual may feel that the drive is an obligation to family, for example, strolling youngsters to class or driving a mate to work. contracted and committed time clients may feel that their commute could really compare to the commute of important or leisure time clients on the grounds that their commute is profitable work. in this manner, they might be more disposed to pick a mechanized method of movement.