An object is moving with a velocity of 5m-1. At what height must a similar body be situated to have a potential energy equal in value with kinetic energy of...

An object is moving with a velocity of 5m-1. At what height must a similar body be situated to have a potential energy equal in value with kinetic energy of the moving body?

Answer Details

To solve this problem, we need to use the conservation of mechanical energy principle, which states that the total mechanical energy of a system (the sum of potential and kinetic energy) remains constant if there are no external forces acting on the system. Let's first calculate the kinetic energy of the moving object. The kinetic energy formula is KE = 0.5 * m * v^2, where m is the mass of the object and v is its velocity. Since we are not given the mass of the object, we can assume it to be 1 kg (since the mass does not affect the height at which the other object must be situated). Therefore, the kinetic energy of the moving object is: KE = 0.5 * 1 * (5)^2 = 12.5 Joules Now, we need to find the height at which the other object must be situated to have the same amount of potential energy as the kinetic energy of the moving object. The potential energy of an object is given by the formula PE = m * g * h, where m is the mass of the object, g is the acceleration due to gravity (9.8 m/s^2), and h is the height at which the object is situated. We want to find the height h at which PE = KE, so we can equate the two formulas: m * g * h = 0.5 * m * v^2 Canceling out the mass on both sides, we get: g * h = 0.5 * v^2 Plugging in the values, we get: h = (0.5 * v^2) / g h = (0.5 * 5^2) / 9.8 h = 1.275 m Therefore, the height at which the other object must be situated to have the same amount of potential energy as the kinetic energy of the moving object is 1.275 meters. The closest option to this answer is 1.3m, so the correct answer is (C) 1.3m.