Question

PLEASE HELP ME!!!!
Michelle and Maggie are at baseball practice. Michelle throws a ball into the air, and when it drops to a height of 5ft, she hits the ball. The height of the ball is modeled by the graph below where t = time in seconds and h = height of the ball from the ground.

Maggie is throwing a ball into the air and catching it. The height of Maggie’s ball is modeled by the function h(t) = –16t2 + 48t + 15.

Part 1. Which ball goes higher in the air, the ball that is hit or the ball that is thrown? Use complete sentences, and show all work to explain how you determined the height that each ball

Answer 1

reaches.

Part 2. Determine which girl is likely to be standing on a raised platform. Use complete sentences to explain how you determine which girl is on the platform, and then determine the height of the platform.

Part 3. Which ball is traveling at a faster average rate of change on the way up? Use complete sentences to explain how you determined the interval at which the height of the ball is increasing and the average rate of change.

Answer 2

part#1
here ve have to compute the vertex of the second parabola, of the Maggie ballfirst

Answer 3

we have to start from the equation:
h(t) = –16t2 + 48t + 15.

Answer 4

okay

Answer 5

If we write a parabola as:
z= at^2+bt+c
then the z-coordinate of the vertex, is:
\[ \large - \frac{{{b^2} - 4ac}}{{2a}}\]

Answer 6

so, substituting our data, we get:
\[\large - \frac{{{b^2} - 4ac}}{{2a}} = - \frac{{{{48}^2} - 4 \times \left( { - 16} \right) \times 15}}{{2 \times \left( { - 16} \right)}} = - \frac{{2304 - 960}}{{ - 32}} = 42\;feet\]

Answer 7

So the ball went 42 feet in the air?

Answer 8

yes!

Answer 9

How do we do that with the other one though

Answer 10

Now, the z-coordinate, of the Michelle's parabola is about 21 feet, so we can conclude that Maggie's ball goes higher

Answer 11

the z-coordinate of the vertex, of the Michelle's parabola

Answer 12

Okay so for part 2 what do i say because i don't know how to tell if one of them is on a platform

Answer 13

if we set t=0, into the formula of Maggie's parabola, we get:
h(0)=15 feet
that is the iniatial height of the Maggie's ball
whereas, the initial height of Michelle's ball is 5 feet
so I think that, since 15>5, then Maggie is standing on arise platform

Answer 14

oops..initial*

Answer 15

Okay now part 3

Answer 16

part #3
here we have to note that Michelle's ball reaches the maximum height after 1 second from the initial shot, (please see the graph).
Whereas Maggie's ball reaches the maximum height after
\[\large t = - \frac{b}{{2a}} = - \frac{{48}}{{2 \times \left( { - 16} \right)}} = \frac{{48}}{{32}} = \frac{3}{2} = 1.5\;\sec \]

Answer 17

ao we can conclude that Michelle's ball is travelling faster than Maggie's ball

Answer 18

Okay thank you so much for the help

Answer 19

Thank you!