A metal block of mass 3 kg is falling downward and has velocity of 0.44 m/s when it is 0.8 m above the floor. It strikes the top of a relaxed vertical spring of length 0.4 m. The spring constant is 2000 N/m. After striking the spring, the block rebounds. What is the maximum height above the floor that the block reaches after the impact

Explanation:

Let assume that one end of the spring is attached to the ground. The speed of the metal block when hits the relaxed vertical spring is:

The maximum compression of the spring is calculated by using the Principle of Energy Conservation:

After some algebraic handling, a second-order polynomial is formed:

The roots of the polynomial are, respectively:

The first root is the only solution that is physically reasonable. Then, the elongation of the spring is:

The maximum height that the block reaches after rebound is: