We can use the principle of conservation of energy, which states that the total energy of a system remains constant if there are no external forces acting on it. In this case, the initial kinetic energy of the object is:
K1 = (1/2) * m * v1^2
K1 = (1/2) * 50.0 kg * (11.2 m/s)^2
K1 = 31,360 J
After the transfer of 1,539 J of energy as work, the final kinetic energy of the object is:
K2 = K1 - W
K2 = 31,360 J - 1,539 J
K2 = 29,821 J
The final velocity of the object can be found by rearranging the kinetic energy equation:
K2 = (1/2) * m * v2^2
v2^2 = (2 * K2) / m
v2^2 = (2 * 29,821 J) / 50.0 kg
v2^2 = 3,585.68 m^2/s^2
Taking the square root of both sides, we get:
v2 = √(3,585.68 m^2/s^2)
v2 = 59.90 m/s
the new velocity of the object after the transfer of energy as work is approximately 59.90 m/s.