Final answer:
To find the speed at the bottom of the ramp, we can use the principles of physics. By equating the potential energy at the top to the kinetic energy at the bottom, we can solve for the velocity at the bottom of the ramp. Using the given values and trigonometry, we can calculate the height of the ramp and then determine the velocity.
Step-by-step explanation:
To find the speed of the skateboarder at the bottom of the ramp, we can use the principles of physics. Since we are neglecting friction, we can assume that the mechanical energy of the skateboarder is conserved. The mechanical energy consists of both kinetic energy and potential energy. At the top of the ramp, the skateboarder has only potential energy, which is given by the formula: potential energy = mass * gravity * height. At the bottom of the ramp, the skateboarder has only kinetic energy, which is given by the formula: kinetic energy = 1/2 * mass * velocity^2. By equating the potential energy at the top to the kinetic energy at the bottom, we can solve for the velocity at the bottom of the ramp.
In this case, the mass of the skateboarder is not provided, but it cancels out when equating the potential and kinetic energies. So we can assume any mass value as long as it is consistent throughout the calculation. Let's assume the mass of the skateboarder is 1 kg for simplicity. The height of the ramp is not provided, but we can calculate it using trigonometry. The height is the vertical component of the ramp's length, which is given by: height = length * sin(angle). Plug in the values and calculate the height.
Next, we calculate the potential energy at the top of the ramp using the calculated height. The potential energy is then equated to the kinetic energy at the bottom of the ramp and solve for the velocity. Plug in the values and calculate the velocity at the bottom of the ramp.