homework problem

Question

A ball is thrown vertically into the air with an initial kinetic energy of 2,500 joules [J]. As the ball rises, it gradually loses kinetic energy as its potential energy increases. At the top of its flight, when its vertical speed goes to zero, all of the kinetic energy has been converted into potential energy. Assume that no energy is lost to frictional drag, etc. How high does the ball rise in units of meters [m] if it has a mass of 5 kilograms [kg]?

The ball rises by................ m. (Round your answer to two significant digits.)

Answer 1

Apply conservation of energy.  Set the initial kinetic energy at the bottom equal to the potential energy at the top, and solve for the height.

 

K = mv²/2 = mgh

 

v²/2 = gh

 

v²/2 = (mv²/2) / m = K/m ⇒

 

gh = K/m

 

h = (K/m) / g = [(2500 J)/(5 kg)] / (9.8 m/s²) ≅ 51.0 meters