Answer:
A. 48 s
B. i. The period tells me that it takes the ride less than one minute to complete the ride.
ii. this tells me that the maximum height of the ride above the ground is 51 + 45 = 96 feet.
Step-by-step explanation:
A. Find the period of the model
Since H(t)= 51 + 45sin ( (π/12)t - π/2), let be period of the motion be T. The first maximum value of sin ( (π/12)t - π/2) = 1 is obtained when t = T/4.
Substituting T/4 into sin ( (π/12)t - π/2) = 1, we have
sin ( (π/12)t - π/2) = 1
sin ( (π/12)T/4 - π/2) = 1
(π/12)T/4 - π/2 = sin⁻¹(1)
πT/48 - π/2 = π/2
collecting like terms,
(πT/48 = π/2 + π/2
πT/48 = π
dividing through by π, we have
T/48 = π/π
T/48 = 1
cross-multiplying, we have
T = 48 s
So, the period is T = 48 s
B.
i. What does the period tell you about the ride?
The period tells me that it takes the ride less than one minute to complete the ride.
ii. What does the amplitude tell you about the ride?
Since the amplitude is the coefficient of sin ( (π/12)t - π/2) which is 45 feet, this tells me that the maximum height of the ride above the ground is 51 + 45 = 96 feet.
