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victus00 [196]
3 years ago
6

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 i

s 18 inches. It takes the ball 2 seconds to go from its maximum height to its minimum height. Which model best represents the height, h, of the ball after t seconds?
Mathematics
2 answers:
Westkost [7]3 years ago
6 0

Answer:

The equation for height is

h=32sin(\frac{\pi}{2}t)+14

Step-by-step explanation:

we are given

An iron ball is bobbing up and down on the end of a spring

So, height function must be trigonometric in nature

So, we can use formula

h=Asin(Bt)+D

now, we can find A , B and D

Calculation of A:

maximum height 46 inch

minimum height =18 inch

so,

A=\frac{46+18}{2}=32

Calculation of B:

It takes the ball 2 seconds to go from its maximum height to its minimum height

So, half of time period is 2 sec

\frac{T}{2}=2

T=4

now, we can use period formula

T=\frac{2\pi}{B}

we can find B

4=\frac{2\pi}{B}

B=\frac{2\pi}{4}

B=\frac{\pi}{2}

Calculation of D:

Max=46

min=18

D=\frac{46-18}{2}

D=14

now, we can plug these values into formula

and we get

h=32sin(\frac{\pi}{2}t)+14


Andrei [34K]3 years ago
5 0

Answer:

Required model is  h=32\sin(\frac{\pi}{2}t)+14

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,

h=A\sin(Bt)+D

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

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

T=4

Period is B

T=\frac{2\pi}{B}

4=\frac{2\pi}{B}

B=\frac{2\pi}{4}

B=\frac{\pi}{2}

3) D is the midline

So, Max=46  and min=18

D=\frac{46-18}{2}

D=14

Substituting all the values,

A=32 , D=14 , B=\frac{\pi}{2}

h=A\sin(Bt)+D

h=32\sin(\frac{\pi}{2}t)+14

Therefore, Required model is  h=32\sin(\frac{\pi}{2}t)+14

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