A lightweight vertical spring of force constant k has its lower end mounted on a table. You compress the spring by a distance d, place a block of mass m on top of the compressed spring, and then release the block. The spring launches the block upward, and the block rises to a maximum height some distance above the now-relaxed spring.

a) Find the speed of the block just as it loses contact with the spring. Express your answer in terms of the variables m, d, and constants g, k.

b) Find the total vertical distance that the block travels from when it is first released to when it reaches its maximum height. Express your answer in terms of the variables m, d, and constants g, k.