The equation models the height h in centimeters after t seconds of a weight attached to the end of a spring that has been stretc
hed and then released. a. Solve the equation for t.
b. Find the times at which the weight is first at a height of 1 cm, of 3 cm, and of 5 cm above the rest position. Round your answers to the nearest hundredth.
c. Find the times at which the weight is at a height of 1 cm, of 3 cm, and of 5 cm below the rest position for the second time. Round your answers to the nearest hundredth.
This is the missing equation that models the hieght and is misssing in the question:
<span>h= 7cos(π/3 t) </span>
Answers:
<span>a. Solve the equation for t. </span>
<span>1) Start: h= 7cos(π/3 t) </span>
2) Divide by 7: (h/7) = <span>cos(π/3 t) </span>
3) Inverse function: arc cos (h/7) = π/3 t
4) t = 3 arccos(h/7) / π ← answer of part (a)
b. Find the times at which the weight is first at a height of 1 cm, of 3
cm, and of 5 cm above the rest position. Round your answers to the
nearest hundredth.
<span>1) h = 1 cm ⇒ t = 3 arccos(1/7) / π</span>
t = 1.36 s← answer
2) h = 3 cm ⇒ t = 3arccos (3/7) / π = 1.08s← answer
3) h = 5 cm ⇒ 3arccos (5/7) / π = 0.74 s← answer
c. Find the times at which the weight is at a height of 1 cm, of 3 cm, and of 5 cm below the rest position for the second time.
Use the periodicity property of the function.
The periodicity of <span>cos(π/3 t) is 6. </span><span> </span><span> </span><span>So, the second times are: </span><span> </span><span> </span><span>1) h = 1 cm, t = 6 + 0.45 s = 6.45 s← answer </span>
