A student is skateboarding down a ramp that is 6.0 m long and inclined at 180 with respect to the horizontal. The initial speed of the skateboarder at the top of the ramp is 2.6 m/s. Neglect friction and find the speed at the bottom of the ramp.

The speed at the bottom of the ramp is 2.6m/s

Explanation:

The final velocity can be determined by means of the equations for a Uniformly Accelerated Rectilinear Motion:

(1)

Notice that it is necessary to found the acceleration that can be done by means of Newton's second law:

The acceleration can be found by means of Newton's second law:

Where is the net force, m is the mass and a is the acceleration.

(2)

Force in the x axis:

The component of the weight in the x axis can be gotten by means of trigonometric:

 (3)

Forces in the y axis:

(4)

The component of the weight in the y axis can be gotten by means of trigonometric:

Remember that the weight is defined as:

The normal force can be obtained from equation (4)

Therefore, equation 4 can be rewritten as:

(5)

Then, replacing equation 3 and equation 5 in equation 2 it is gotten:

(6)

However, a can be isolated from equation 6

 (7)

Finally, equation 7 can be replaced in equation 2:

Hence, the speed at the bottom of the ramp is 2.6m/s