Question

Antonio's toy boat is bobbing in the water under a dock. The vertical distance

�
HH (in
cm
cmstart text, c, m, end text) between the dock and the top of the boat's mast
�
tt seconds after its first peak is modeled by the following function. Here,
�
tt is entered in radians.
�
(
�
)
=
5
cos
⁡
(
2
�
3
�
)
−
35.5
H(t)=5cos(
3
2π
​
t)−35.5H, left parenthesis, t, right parenthesis, equals, 5, cosine, left parenthesis, start fraction, 2, pi, divided by, 3, end fraction, t, right parenthesis, minus, 35, point, 5
How long does it take the toy boat to bob down from its peak to a height of
−
35
cm
−35 cmminus, 35, start text, space, c, m, end text?

Answer 1

Answer: To find the time it takes for the toy boat to bob down from its peak to a height of -35 cm, we need to find the value of t when H(t) = -35.

So, we can substitute -35 for H(t) in the given equation:

5 cos (2π/3t) - 35.5 = -35

Now we can solve for t by isolating it on one side of the equation:

5 cos (2π/3t) = 0.5

cos (2π/3t) = 0.1

2π/3t = cos^-1(0.1)

3t = 2π * cos^-1(0.1)/π

t = 2 * cos^-1(0.1)

The time it takes for the toy boat to bob down from its peak to a height of -35 cm is approximately 2 * cos^-1(0.1) seconds.

Explanation: