The skateboarder in the drawing starts down the left side of the ramp with an initial speed of 5.4 m/s. If nonconservative forces, such as kinetic friction and air resistance, are negligible, what would be the height h of the highest point reached by the skateboarder on the right side of the ramp?
1.r
To find the height reached by the skateboarder on the right side of the ramp, we can use the principle of conservation of mechanical energy. This principle states that the total mechanical energy of a system remains constant if only conservative forces are involved.
In this case, since nonconservative forces such as kinetic friction and air resistance are negligible, the total mechanical energy remains constant. The mechanical energy of the skateboarder at the bottom of the ramp is solely in the form of kinetic energy, given by:
KE = (1/2) * m * v^2
where KE is the kinetic energy, m is the mass of the skateboarder, and v is the initial speed.
At the highest point of the ramp, the mechanical energy is in the form of gravitational potential energy, given by:
PE = m * g * h
where PE is the potential energy, g is the acceleration due to gravity, and h is the height reached by the skateboarder on the right side of the ramp.
According to the conservation of mechanical energy, the initial kinetic energy at the bottom of the ramp is equal to the potential energy at the highest point on the right side:
KE = PE
(1/2) * m * v^2 = m * g * h
Now, we can solve for h:
h = (1/2) * v^2 / g
Plugging in the values, where v = 5.4 m/s and g = 9.8 m/s^2, we can calculate h as follows:
h = (1/2) * (5.4)^2 / 9.8
h ≈ 1.47 meters
Therefore, the height reached by the skateboarder on the right side of the ramp is approximately 1.47 meters.