ElectricPavlov

Before the ball is dropped it has POTENTIAL energy = mgh    all of this energy is converted to kintetic energy 1/2 mv^2 at the point where the basketball hits the floor

(original) mgh = 1/2 mv^2(at floor)        I cannot graph these equations here.    g'luck !

For 'B'   it is not a perfectly elastic collision between the ball and the concrete....   some of the energy is lost in making a sound (air vibrations) some of the enrgy is lost in vibrations in the concrete, some of the nergy is lost in deformation of the ball AND the concrete...even though they may spring back to the original shape, this deformation results in heat in the ball and the concrete,  lastly , thee is AIR friction to which the ball loses energy...this results in a minute heating of th air and the ball.

Wow!  The PC Police are out!     HSC,  it is your OPINION that the other two guests are 'simple minded'....you have no real basis for this conclusion.   'retarded' was, for many many years simply a medical term for someone of below average IQ before someone with thin skin decided they thought it was 'not nice' and they were 'offended'.   Now it is called 'Developmentally delayed...or disabled'   and someday some other knothead will become offended by this term and it will morph into something else...but it is what it is, no matter what you want to call it.

Kinda guessing here......If it was just  
't' instead of 5t  it would be a sinusoid with a period of  2 pi   or 360 degrees, because it is a fxn of sin and cos

since it is '5t'   the period will be shortened by '5'     360/5 = 72    period      NO guarantee!  

10   Binary, right?

Well the recipe is for 4 people and you want to make it for 10 ....  or 10/4 = 2 1/2 times as many people   ...so multiply each of the ingredients by 2 1/2  (or 2.5)(or 5/2)

OJ  1/2 cup x 2.5  =  1/2 x 5/2  = 5/4 = 1 1/4  cups

Pineappple     1 cup x 2 1/2   = 2 1/2 cups

syrup   1/3 cup x  5/2  = 5/6 = 1 1/6 cups

when t = 21.688      x = 0

Sure      x= 0    =   12cos(5t) + 4sin(5t)

re-arranging           12cos(5t) = -4sin5t

                               -12/4 =  sin5t / cos5t      (remember sin/ cos = tan)

                                -3      =  tan5t

                            Arctan(-3) = 5t

                                    -71.565   or 108.43 (this is the only answer between 0 and pi)   = 5t       t = 21.686   

when t = 21.688      x = 0

If the diameter is 18 inches

the CIRCUMFERENCE is 56.54 inches.... NOT 50.3 cm

10000 miles x 5280 feet/mile x 12 in/foot  / 56.54 in =11204508 rotations