1. The propeller of a boat at dock in the ocean will rise and fall with the waves. On a particularly wavy night, the propeller leaves its resting position and reaches a height of 2.5 m on the peaks of the waves and -2.5 m in the troughs. The time between the peak and the trough is approximately 2 seconds. Determine the equation of a sinusoidal function that would model this situation assuming that at t = 0, the propeller is at its resting position and headed towards the peak of the next wave. INClude Sketch and what is the Period

5: A potato cannon launches a potato straight up from a height of 5 feet with an initial velocity of 128 ft/sec. The horizontal distance from the cannon launch and the vertical height from the ground, in feet, are modeled by a set of parametric equations. . Write a set of parametric equations that will model the height of the potato as a function of time, t. . Find the average rate of change in horizontal position over the first two seconds. Show your work and units. What is the average rate of change in vertical motion over the first two seconds? Show your work and units.

Suppose that a bee is approaching a flower following the trajectory x = t° – 3t, y = t². Please note: Parts (a) and (b) should be written on one page, parts (c) and (d) - on the next page. (a) Find equation(s) of the tangent line(s) at (0, 3); (b) Find the coordinates of the points where the bee is flying horizontally and vertically; (c) Where is the trajectoty concave up and down? (d) Draw a rough sketch of the trajectory, indicating your findings about tangent lines. Hint: Use values of t = +2, ±V3, ±1,0.

2. A Ferris wheel has a radius of 40 feet and is boarded in the 6 o'clock position from a platform that is 5 feet above the ground. The wheel completes a counterclockwise revolution every 2 minutes. At t=0 the person is at the 3 o'clock position.