When an ideal spring is compressed or stretched, it stores potential energy that can be converted into kinetic energy when the spring is released. The amount of potential energy stored in the spring can be calculated using the formula:
U = (1/2) k x^2
where U is the potential energy, k is the spring constant, and x is the displacement of the spring from its equilibrium position.
In this problem, the potential energy stored in the spring is converted into kinetic energy of the block as it is launched horizontally. The kinetic energy of the block can be calculated using the formula:
K = (1/2) mv^2
where K is the kinetic energy, m is the mass of the block, and v is the velocity of the block.
We can equate the potential energy stored in the spring to the kinetic energy of the block as follows:
(1/2) k x^2 = (1/2) mv^2
Substituting the given values, we get:
(1/2) (450.2 N/m) (0.132 m)^2 = (1/2) (0.091 kg) v^2
Simplifying this equation and solving for v, we get:
v = √[(450.2 N/m) (0.132 m)^2 / 0.091 kg]
v = 1.527 m/s
Therefore, the block is moving horizontally with a speed of 1.527 m/s when it leaves the spring.