Question

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.

Answer 1

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 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

@mathstudent55

Answer 3

@surjithayer

Answer 4

@TuringTest

Answer 5

@hoblos

Answer 6

@aaronq

Answer 7

to answer this we need the graph of Michelles's ball

Answer 8

Which ball goes higher in the air?
The first step is to find how high the ball goes for each:

For Maggie, we have the equation
\[ h(t) = –16t^2 + 48t + 15 \]

find the vertex. Do you know how ? the x value of the vertex is -b/(2a)

Answer 9

for maggie
h=-16t^2+48t+15
\[\frac{ dh }{dt }=-32t+48=0,t=\frac{ 48 }{32 }=\frac{ 3 }{2 }seconds\]
when t=3/2 s
h=-16(3/2)^2+48*3/2+15=?

Answer 10

at maximum height velocity =0

Answer 11

I assume you don't know calculus (what surji) did. But can you figure out what h is when you set t= 3/2 ?

Answer 12

If for some reason it is inconvenient to plug in the variable, you can also get the y value of the vertex from \[y = c-\frac{b^2}{4a}\]

Answer 13

how would I answer part 1?

Answer 14

you need to figure out what h is in
h=-16(3/2)^2+48*3/2+15=?