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

This is the graph

I don't know what the first paragraph is talking about though... it might be a mistake.

Answer 3

@Nnesha @triciaal @zepdrix @mathmale @mathstudent55 @sleepyjess @ganeshie8

Answer 4

@boldjon @EclipsedStar @satellite73

Answer 5

Can someone help?

Answer 6

Working on it

Answer 7

@Blacksteel K, thanks!

Answer 8

the first paragraph and the graph is for Michelle's
the function given is for Maggie's

Answer 9

Oh

Answer 10

@Blacksteel will continue

Answer 11

Ah, now i kinda get it. Michelle's thing is represented by a graph, Maggie's is represented by an equation

Answer 12

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.

Answer 13

h(t) = –16t2 + 48t + 15

Answer 14

The vertex for the graph can be easily found. The vertex for the equation can be put into

-2/ba and then the x coordinate of the vertex can be put into h(t) = –16t2 + 48t + 15 as t.

Answer 15

And that solves Part A

Answer 16

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.

Answer 17

This can be determined by finding the y-intercept

Answer 18

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 19

\[\frac{ Rise }{ Run }\]

Answer 20

One question though

Answer 21

Part 1:
So the height of Michelle's ball as a function of time is given by the graph. The maximum height, or x value, of the ball is ~21.
The height of Maggie's ball is given by the function h(t) = -16t^2 +48t + 15. That means the rate of change of height is given by the derivative of this function., h'(t) = -32t + 48. When this function is 0, the ball is changing from rising to falling, or vice versa. Since we know that the ball starts by rising and only changes direction once, this function's only root (0 value) will by at the time it starts to fall, which is when the ball is at it's maximum height.
So 0 = -32t + 48 => 32t = 48 => t = 1.5. This tells us that the maximum height of the ball occurs at t = 1.5. We can plug this value into the original function to find out what that height is:
h(1.5) = -16(1.5^2) + 48(1.5) + 15 = -36 + 72 + 15 = 51

Since 51 is much larger than 21, Maggie's ball goes higher.