Question

A marching band performs on the football field at half-time. As they perform, the members of the band stand in theshape of a sinusoidal function. While playing, they move, but still maintain the sinusoidal function, transforming itin different ways.Darla is a member of the marching band. As the band begins to play she is positioned in the exact center of thefield. The person closest to her on the same horizontal line, stands 10 yards away. The sinusoidal functionextends to the ends of the playing field.The playing area of football field measure 300 feet by 160 feet. Place the playing area of a football field on thecoordinate plane such that the origin is the lower left corner of the football field.

Answer 1

1. a. For amplitude and period:

Here, we are told that the wave reaches the end of the field. To find the amplitude, use the formula:

`(1)/(2)\text{ of W}`

where W is width and W = 160 feet

Thus, amplitude =

`(1)/(2)\ast\text{ 160 = 80 feet}`

since the closest person on the horizontal line is 10 yards away. The period will be:

first convert 10 yards to feet, since 1 yard = 3 feet,

10 yards = 10 * 3 feeet = 30 feet

period = 2 * 30 feet

Period = 60 ft

Therefore,

amplitude = 80 ft

Period = 60 ft