4. elijah does 44 joules of work against gravity to pull a 0.5-kilogram rope with a 1.0-kilogram bucket attached up to the floor of his tree house. how many meters high is his tree house?

Given: Work W = 44 J;   Mass of the rope and the bucket  m= 1.5 Kg

Required: Find the height in meters  

Formula: Work = Force x distance   but  Force = Weight = mg  g = 9.8 m/s²

W =Fd  W = mgh    h = W/mg  

h = 44 J/(1.5 Kg)(9.8 m/s²)

h = 2.99 m or 3 m

Kinetic energy = 1/2mv^2. since the mass is constant we can form a ratio of it's kinetic energy at 60 divided by that at 30 to see ke(60)/ke(30) = +(60^2)/30^2). this may be said to 300% increase.

Wavelength divides in half and speed stays the same.