SOLUTION: I am so confused my head hurts please help me. Suppose you throw a baseball straight up at a velocity of 64 feet per second. A function can be created by expressing distance abo

Question 42073This question is from textbook college algebra gary rockswold
: I am so confused my head hurts please help me.
Suppose you throw a baseball straight up at a velocity of 64 feet per second. A function can be created by expressing distance above the ground, s, as a function of time, t. This function is s = -16t2 + v0t + s0
• 16 represents 1/2g, the gravitational pull due to gravity (measured in feet per second2).
• v0 is the initial velocity (how hard do you throw the object, measured in feet per second).
• s0 is the initial distance above ground (in feet). If you are standing on the ground, then s0 = 0.

a) What is the function that describes this problem?
Answer:

b) The ball will be how high above the ground after 1 second?
Answer:
Show work in this space.

c) How long will it take to hit the ground?
Answer:
Show work in this space.

d) What is the maximum height of the ball? What time will the maximum height be attained?
Answer:
Show work in this space.

4) John has 300 feet of lumber to frame a rectangular patio (the perimeter of a rectangle is 2 times length plus 2 times width). He wants to maximize the area of his patio (area of a rectangle is length times width). What should the dimensions of the patio be, and show how the maximum area of the patio is calculated from the algebraic equation.
Show clearly the algebraic steps which prove your dimensions are the maximum area which can be obtained.
Answer:
Show work in this space. This question is from textbook college algebra gary rockswold

Answer by josmiceli(6786) (Show Source):
You can put this solution on YOUR website!
I can solve the 1st one

v(0) = 64 ft/sec

v(0) = 64 ft/sec
after 1 sec

The ball is 48 ft high after 1 sec
How long will it take to hit the ground?
The curve for this equation is a parabola with time
plotted horizontally and distance vertically
You want to find BOTH times when s=0. The first
is t=0, when the ball leaves the throwers hand.
The second time s=0 is when the ball returns to
ground.

rewrite

the roots are
t = 0 (ball leaves hand)
t = 4 (ball returns to ground)
The ball takes 4 sec to return to earth
What is the maximum height of the ball?
What time will the maximum height be attained?
The vertex of the parabola is the max height
The vertex occurs midway between t=0 and t=4, or t=2

The max height is 64 ft, 2 sec after ball is thrown