Question

Another object moves in the air along the path of g(t) = 28 + 48.8t where g(t) is the height, in feet, of the object from the ground at time t seconds.

Use a table to find the approximate solution to the equation H(t) = g(t), and explain what the solution represents in the context of the problem? [Use the function H(t) obtained in Part A, and estimate using integer values] (4 points)

Part D: Do H(t) and g(t) intersect when the projectile is going up or down, and how do you know?

Answer 1

@Michele_Laino

Answer 2

this is what i have so far the equation would be H(t)=-16x^2+50t+90

Part B: When you graph the equation its highest point is about (1.5,129) so about 129 feet above the ground is the highest point it will reach its maximum at 1 and 1/2 seconds.

Answer 3

like these are before those up there and i have them answered and these are follow up questiosn to my answers above

Answer 4

we can write the subsequent equation:

\[\Large - 16{t^2} + 50t + 90 = 28 + \frac{{244}}{5}t\]
since:
48.8= 244/5

Answer 5

now I multiply both sides by 5 and I get:
\[\Large - 80{t^2} + 250t + 450 = 140 + 244t\]

Answer 6

alright

Answer 7

i have to make a table tho.

Answer 8

yes! nevertheless you have to use this equation:
\[\Large - 16{t^2} + 50t + 90 = 28 + \frac{{244}}{5}t\]

Answer 9

ohh okay.

Answer 10

better is to plot a graph of each of your functions

Answer 11

i did so already

Answer 12

where do your graphs intersect each other?

Answer 13

(2,126)

Answer 14

about there

Answer 15

then you can try to consider the subsequent values of t:
T=1.8, t= 1.9. t=2.0, and t=2.1, namely you have to substitute those values of t, into this equation:
\[\Large - 16{t^2} + 50t + 90 = 28 + \frac{{244}}{5}t\]

Answer 16

im really confused on how to make the table??

Answer 17

here is your table:

you have to find the values of H(t), and g(t) at t=1.8, 1.9, 2.0, and 2.1

Answer 18

oh okay!!

Answer 19

better is if you add another value of t, like this:

Answer 20

when you have done, please tag me

Answer 21

for 1.8 i got 128 and 115
so for 1.9 i got 127 and 120
for 2.0 i got 126 and 126
for 2.1 i got 125 and 130

Answer 22

@Michele_Laino

Answer 23

then the requested solution is t=2.0, since:
H(2.0)=g(2.0)=126

Answer 24

for part D, we can find the x-coordinate of the vertex of the parabola H(t):
we have
x=25/16 which is less than 2, so the intersection between the graphs of your functions, occurs when the projectile is going down