Final answer:
To reach the upper edge of a half-pipe, the skateboarder needs an initial speed of approximately 3.83 m/s. This calculation is based on the conservation of energy, equating the kinetic energy at the bottom with the potential energy at the height of the half-pipe.
Step-by-step explanation:
Calculating the Initial Speed Required for a Skateboarder
To find the skateboarder's initial speed to reach the upper edge of a half-pipe, we will use the conservation of energy principle. The potential energy at the top of the half-pipe (due to gravity) must equal the kinetic energy (due to motion) at the bottom of the half-pipe, minus any energy lost to friction (which we assume to be negligible in this question).
The skateboarder needs enough initial kinetic energy to convert into gravitational potential energy to reach the top of the half-pipe. The gravitational potential energy (PE) at the top is given by the formula PE = mgh, where m is the mass of the skateboarder, g is the acceleration due to gravity (9.8 m/s2), and h is the vertical height of the half-pipe. The initial kinetic energy (KE) at the bottom is given by KE = 0.5mv2, where v is the initial velocity we are trying to find.
To solve for the initial velocity, we set the kinetic energy equal to the potential energy and solve for v:
We are given that the height h is 0.75 m, so we substitute this into the equation along with the gravitational acceleration:
Therefore, the skateboarder would need an initial speed of approximately 3.83 m/s to reach the upper edge of the half-pipe.