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?
what is the answer?
To find the height h of the highest point reached by the skateboarder on the right side of the ramp, we can use the principle of conservation of mechanical energy. According to this principle, the total mechanical energy of a system remains constant if nonconservative forces, such as friction and air resistance, are negligible.
The mechanical energy of the skateboarder at any point can be divided into two components: kinetic energy (KE) and potential energy (PE).
At the highest point reached by the skateboarder, all of the initial kinetic energy will be converted into potential energy. Therefore, we can equate the initial kinetic energy to the potential energy at the highest point.
The formula for kinetic energy is:
KE = (1/2)mv^2
where m is the mass of the skateboarder and v is the initial speed.
Since the mass is not given in the question, and it is not necessary to find the height h, we can ignore it in our calculations. Therefore, the formula for kinetic energy becomes:
KE = (1/2)v^2
The potential energy at the highest point is given by the formula:
PE = mgh
where g is the acceleration due to gravity (approximately 9.8 m/s^2) and h is the height.
Since the initial kinetic energy is converted entirely into potential energy at the highest point, we can equate them:
(1/2)v^2 = mgh
Now, we need to solve for h. Rearranging the equation, we have:
h = (1/2)v^2 / (mg)
Substituting the given values, v = 5.4 m/s and g = 9.8 m/s^2, we can calculate the height h:
h = (1/2)(5.4 m/s)^2 / (9.8 m/s^2)
h ≈ 1.46 meters
Therefore, the height h of the highest point reached by the skateboarder on the right side of the ramp is approximately 1.46 meters.