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Question: Ryan Gosling is jumping on a trampoline. His distance from the ground, in metres, in terms of time, is modelled by the equation h(s) = 0.75cos(180s)° + 1.5. What does the 1.5 in this equation represent?

The equation \( h(s) = 0.75\cos(180s)° + 1.5 \) describes Ryan Gosling's height in meters at any given time \( s \) while he is jumping on a trampoline. In this equation: - \( 0.75\cos(180s)° \) represents the oscillating component of his height due to his motion on the trampoline, where the amplitude of oscillation is 0.75 meters. - The \( 1.5 \) is a constant. The \( 1.5 \) meters in this equation represents the vertical shift or the midpoint around which Ryan's height oscillates. It is the average height from the ground level when he is at the midpoint of his jump, assuming the trampoline mat is at 0 meters. Essentially, it is the height of the trampoline mat when he is at rest, or the average height above the ground when he is on the trampoline.

The 1.5 in the equation represents the base height or the baseline distance from the ground when not jumping. It means that even when Ryan is not jumping (when the cosine function is at its minimum), he is still 1.5 meters above the ground. This could be due to the height of the trampoline off the ground or his height from the feet to his center of mass.

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