Final answer:
Using the conservation of mechanical energy, a skateboarder traveling up a ramp with an initial velocity of 11 ft/sec can reach a maximum vertical height of approximately 1.88 feet.
Step-by-step explanation:
To determine the vertical height someone can reach on a skateboard if their velocity at the bottom of a ramp is 11 ft/sec, we can use the principles of physics, specifically the conservation of mechanical energy. Assuming no friction or air resistance, the skateboarder's kinetic energy at the bottom of the ramp is transformed into potential energy at the highest point of their trajectory. The formula to calculate the height is given by the equation KE = PE, where KE is kinetic energy (0.5 * m * v^2) and PE is potential energy (m * g * h).
To find the height (h) we need to solve for h in the equation m * g * h = 0.5 * m * v^2. Since the mass (m) cancels out, we simply solve for h as h = v^2 / (2 * g), with v being the initial velocity (11 ft/sec) and g representing the acceleration due to gravity (32.2 ft/sec^2).
Calculating the Maximum Height
h = (11 ft/sec)^2 / (2 * 32.2 ft/sec^2) = 121 / 64.4 ≈ 1.88 ft
Therefore, the skateboarder can reach a maximum vertical height of approximately 1.88 feet.