Mathematics
07.03.2022 20:00
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mattmore0312
mattmore0312
5,0(37 marks)

H(t)= 5cos(\pi(t-0.2))-20

Step-by-step explanation:

Let the function be a cosine function

H(t)= A cos(B(t+C)) + D

Average height = -20 cm

The object's maximum and minimum heights are each 5 cm from its average height. Therefore:

Maximum Height, H_{max}=-20+5=-15cm

Minimum Height ,  H_{min}=-20-5=-25cm

The amplitude, A is denoted by :

A=\dfrac{H_{max}-H_{min}}{2} \\=\dfrac{-15-(-25)}{2}=(-15+25)\div 2 =5\\A=5

The vertical shift, D is denoted by :

D=\dfrac{H_{max}+H_{min}}{2} \\=\dfrac{-15+(-25)}{2}=(-15-25)\div 2 =-20\\D=-20

The period T is given by,

T=2 seconds

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

The phase shift , C is given by:

C=-0.2 (since it first achieves its average height to the right at t=0.2 sec)

Therefore, our function is defined as:

H(t)= 5cos(\pi(t-0.2))-20

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