Question

You are on in-line skates at the top of a small hill. Your potential energy is equal to 1,000 J. The last time you checked, your mass was 60.0 kg.If you start rolling down this hill, your potential energy will be converted to kinetic energy. At the bottom of the hill, your kinetic energy will be equal to the potential energy at the top. Calculate your speed at the bottom of the hill.

Answer 1

To find the speed at the bottom of the hill, we can use the equation for gravitational potential energy and the equation for kinetic energy. By equating the two energies, we can solve for the velocity at the bottom of the hill. In this case, the speed at the bottom of the hill is 8.16 m/s.

Step-by-step explanation:

To calculate the speed at the bottom of the hill, we need to use the principle of conservation of energy. The potential energy at the top of the hill is converted into kinetic energy at the bottom. The formula for gravitational potential energy is PE = mgh, where m is the mass, g is the acceleration due to gravity (approximately 9.81 m/s^2), and h is the height. In this case, the potential energy is 1,000 J, the mass is 60.0 kg, and g is 9.81 m/s^2. Solving for h, we get h = PE / (mg) = 1,000 J / (60.0 kg * 9.81 m/s^2) = 1.68 m.

To find the speed at the bottom of the hill, we can use the equation for kinetic energy: KE = (1/2)mv^2, where KE is the kinetic energy, m is the mass, and v is the velocity. In this case, the kinetic energy is equal to the potential energy, so we can set them equal to each other: 1,000 J = (1/2) * 60.0 kg * v^2. Solving for v, we get v = sqrt((2 * 1,000 J) / (60.0 kg)) = 8.16 m/s.