Shaw’s carries two types of apple juice. One is 100% fruit juice, while the other is only 40% juice. Yesterday there was only one 48-ounce bottle of the 100% juice left. I bought it, along with a 32-ounce bottle of the 40% juice. I am about to mix the contents of the two bottles together. What percent of the mixture will be actual fruit juice?

the percent of actual fruit juice in the mixture will be 76%

Explanation:

given that we are mixing 2 bottles the total volume the mixture will be

mixture volume = volume bottle 1 + volume bottle 2  = 48 ounces +  32 ounces = 80 ounces

also the total quantity of juice will be

juice mass in mixture = juice bottle 1  + juice bottle 2 = 48 ounces * 1 +  32 ounces * 0.4 = 60.8 ounces of juice

therefore the concentration of juice in the mixture will be

concentration = 60.8 ounces of juice / 80 ounces = 0.76 (76%)

therefore the percent of actual fruit juice in the mixture will be 76%

h

first let us lay out the formula for potential

and kinetic energy:

pe = mgh

ke = (mv^2)/2

where: m=mass, v=velocity, g=gravitational

acceleration, h=height

calculating for mass using the known values of

pe:

340j = m (9.81 m/s^2) (50ft) (1m/3.28ft)

m = 2.27 kg

the law of conservation of energy states that

energy is neither created nor destroyed. therefore, the change in kinetic

energy from 50 ft to 35 ft would be equal to the change in potential energy

from 50 ft to 35 ft. however it would be opposite in signs since one is losing

while other is gaining.

ke(35ft) – ke(50ft) = - [ pe(35ft) – pe(50ft]

ke(50ft) = 0 since the brick is initially at rest

ke(35ft) = 340j - 2.27kg (9.81 m/s^2) (35ft)

(1m/3.28 ft)

ke(35ft)

= 102.38 j