The equation is s=144t - 16t², s being the distance and V=144 ft/s
a)The maximum (or minimum) is reached when the derivative of s = 0
s' = 144 - 32t = 0 and t= 9/2 or 4.5 second (time needed to reach the max
Now plug t= 4.5 in the original equation and you will find s = 324 ft
(Why it's a max and not a minimum: because 2nd derivative is negative and equals s" = -32)
b) Velocity of the ball: distance (up) s=320 ft, time that means:
320 =144t - 16t² (solve for x) -16t²+144t-320 = 0, t₁ =4 and t₂ =5 (t₂ is not valid since max time to reach summit is 4.5) so t =4s , distance = 320. so the velocity at 320ft is 320/4 = 80 ft/s
c) Due to the symmetry of the parabola, the velocity at 320 ft on its way down = 80 ft/s
I found the common multiple which was 12 so I multiplied 12 to all the fractions which gave an improper fraction that turned into a whole number. I hope this helps if you have any questions just ask me and I will answer.
The reciprocal of a fraction is only a whole number when
the numerator of the original fraction is ' 1 ' or a factor of
the denominator (original fraction is not in simplest form).
Any other time, the reciprocal of the fraction is another fraction.
(It'll be an improper fraction, and can be written as a mixed number.)
The reciprocal of a fraction is just the same fraction
turned upside down.
-- The reciprocal of 1/5 is 5/1 or just 5 .
(Original numerator is ' 1 '.)
-- The reciprocal of 5/25 is 25/5 or just 5 .
(Original fraction is not in simplest form.)
-- The reciprocal of 5/7 is 7/5 , or 1 and 2/5 .
Answer: (4) d=112 (7) 2.75 or 2 3/4
explanation: pictured below
