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?
To find the height h of the highest point reached by the skateboarder on the right side of the ramp, we can apply the principle of conservation of mechanical energy. This principle states that the total mechanical energy of an object in the absence of nonconservative forces remains constant.
The mechanical energy of an object can be expressed as the sum of its kinetic energy (KE) and potential energy (PE). In this case, we assume the skateboarder starts from the left side with only kinetic energy, and by the time they reach the highest point on the right side, all their initial kinetic energy is converted into potential energy.
First, let's find the initial kinetic energy of the skateboarder:
KE = 1/2 * m * v^2
where m is the mass of the skateboarder and v is the initial velocity.
Next, we can equate the initial kinetic energy to the potential energy at the highest point:
KE = PE
m * v^2/2 = m * g * h
where g is the acceleration due to gravity.
By substituting the given values, we can solve for h:
m * (5.4 m/s)^2/2 = m * 9.8 m/s^2 * h
Canceling out the mass (m) on both sides:
5.4 m/s * 5.4 m/s/2 = 9.8 m/s^2 * h
h = (5.4 m/s * 5.4 m/s) / (2 * 9.8 m/s^2)
Simplifying the calculation:
h = (29.16 m^2/s^2) / (19.6 m/s^2)
Finally, dividing:
h ≈ 1.49 meters
Therefore, the height (h) of the highest point reached by the skateboarder on the right side of the ramp is approximately 1.49 meters.