A soccer ball on the ground was kicked with an initial velocity of 35 ft/sec at an elevation angle of 40°. Create a set of parametric equations to model the path of the soccer ball. Approximately how far had the soccer ball traveled when it hit the ground?

Using gravity of 32 ft/s², the horizontal and vertical components of the initial velocity are 35 cos(40°) and 35 sin(40°). A parametric model is x(t) = 35 cos(40°)t and y(t) = 35 sin(40°)t − 16t², for t ≥ 0. The ball returns to the ground when y(t) = 0, giving t = 70 sin(40°)/32 ≈ 1.41 seconds. Then x ≈ 35 cos(40°)(1.41) ≈ 37.7 feet, so the ball traveled about 38 feet (choice C).

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