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Hyun Woo is riding a ferris wheel. H t H(t) models his height (in m m) above the ground, t t seconds after the ride starts. Here, t t is entered in radians. H t 1 0 cos 2 ? 1 5 0 t 1 0 H(t)=?10cos( 150 2? ? t)+10 When does Hyun Woo first reach a height of 1 6 m 16 m? Round your final answer to the nearest whole second.

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Edufirst

Answer:

  • 53 seconds.

Explanation:

The text and the model are garbled.

This is the question amended:

Hyun Woo is riding a ferris wheel. H(t) models his height (in m) above the ground, t seconds after the ride starts. Here, t is entered in radians.

H(t) = -10 cos(2π/150 t)+10

When does Hyun Woo first reach a height of 16 m?

Solution

When Hyun Woo reaches a height of 16 m the model states:

  • 16 = -10 cos(2π/150 t)+10

Then you must find the lowest positive value of t that is a solution of the equation.

Solve the equation:

  • 16 = -10 cos(2π/150 t)+10

  • 10cos(2π/150 t) = - 6

  • cos(2π/150t) = -0.6

  • 2π/150t = arccos(-0.6)

  • 2π/150t = 2.214297

  • t = 52.86s ≈ 53 s ← answer

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