Answer:
Required model is
Step-by-step explanation:
Given : An iron ball is bobbing up and down on the end of a spring. The maximum height of the ball is 46 inches and its minimum height is 18 inches. It takes the ball 2 seconds to go from its maximum height to its minimum height.
To find : Which model best represents the height, h, of the ball after t seconds?
Solution :
According to question,
The height function must be trigonometric in nature.
So, we can use formula,
Now, We calculate A,B and D
1) Maximum height 46 inch
Minimum height =18 inch
Average height is A
![A=\frac{46+18}{2}=32](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B46%2B18%7D%7B2%7D%3D32)
2) It takes the ball 2 seconds to go from its maximum height to its minimum height
So, half of time period is 2 sec
i.e, ![\frac{T}{2}=2](https://tex.z-dn.net/?f=%5Cfrac%7BT%7D%7B2%7D%3D2)
![T=4](https://tex.z-dn.net/?f=T%3D4)
Period is B
![T=\frac{2\pi}{B}](https://tex.z-dn.net/?f=T%3D%5Cfrac%7B2%5Cpi%7D%7BB%7D)
![4=\frac{2\pi}{B}](https://tex.z-dn.net/?f=4%3D%5Cfrac%7B2%5Cpi%7D%7BB%7D)
![B=\frac{2\pi}{4}](https://tex.z-dn.net/?f=B%3D%5Cfrac%7B2%5Cpi%7D%7B4%7D)
![B=\frac{\pi}{2}](https://tex.z-dn.net/?f=B%3D%5Cfrac%7B%5Cpi%7D%7B2%7D)
3) D is the midline
So, Max=46 and min=18
![D=\frac{46-18}{2}](https://tex.z-dn.net/?f=D%3D%5Cfrac%7B46-18%7D%7B2%7D)
![D=14](https://tex.z-dn.net/?f=D%3D14)
Substituting all the values,
A=32 , D=14 , ![B=\frac{\pi}{2}](https://tex.z-dn.net/?f=B%3D%5Cfrac%7B%5Cpi%7D%7B2%7D)
Therefore, Required model is