To what height would a 2-kg object have to be raised so that its gravitational potential energy would equal the kinetic energy it would possess if it were moving at 3 m/s

Kinetic energy = 0.5mv^2

For the object moving at 3m/s, it has kinetic energy = 0.5*2*3^2 = 9J

Gravitational potential energy = mgh

Assuming g = 9.81 m/s^2, solving for 9J = mgh gives h = 9 / (2*9.81) = 0.459m (3 s. f.)