Question

1. your boat is bobbing slowly in the ocean over the waves while you are fishing. the range of the swells are 4 feet from the top of a swell to the bottom. if it takes you 10 seconds to travel from the top of one wave to the top of the next wave, sketch two complete cycles.

Explanation:

Step1: Determine Amplitude

The range from top to bottom of a swell is 4 feet. Amplitude \( A \) is half the range, so \( A=\frac{4}{2} = 2 \) feet.

Step2: Determine Period

Time to go from top of one wave to top of next is 10 seconds, so period \( T = 10 \) seconds.

Step3: Sketch First Cycle

• Start at \( (0, 2) \) (top of first wave).
• At \( t = 5 \) (half - period), reach \( (5, - 2) \) (bottom of the wave).
• At \( t = 10 \), return to \( (10, 2) \) (top of second wave), completing first cycle.

Step4: Sketch Second Cycle

• From \( t = 10 \) to \( t = 15 \), go from \( (10, 2) \) to \( (15, - 2) \).
• From \( t = 15 \) to \( t = 20 \), go from \( (15, - 2) \) to \( (20, 2) \), completing second cycle.

(Note: To sketch on the given grid, plot the points \((0,2)\), \((5, - 2)\), \((10,2)\), \((15, - 2)\), \((20,2)\) and connect them with a smooth sinusoidal curve.)

Answer:

The graph is a sinusoidal curve with amplitude 2, period 10 seconds. It starts at \((0,2)\), goes to \((5, - 2)\), \((10,2)\), \((15, - 2)\), \((20,2)\) (two complete cycles from \(x = 0\) to \(x=20\) with \(y\) - axis representing height and \(x\) - axis representing time in seconds).