Which of these physical settings makes sense for an object moving along the x-axis? Its position at any time is given by x(t) = 3cos(π t) + 2
a. A skydiver falling from a plane, before she opens her parachute.
b. The shadow cast by a rock that's stuck on the edge of a spinning wheel.
c. A car driving from San Diego to Los Angeles.
d. An ant walking at a steady pace from the tip of a propeller toward the hub.
e. None of these settings.
probably b, right?
yes, probably b, as silly as the example is.
The shadow cast
cosine is an oscillating function, meaning it gets bigger, then smaller, over and over. It is called a circular function because it models the location of a point on a rolling circle.
so, what do you think?
e. None of these settings.
While the given equation describes an object's position along the x-axis, none of the settings provided correspond to this particular mathematical expression. However, if you feel creative, you could imagine a scenario where a clown bot is juggling bananas and as it tosses each banana up and down along a straight line, its position follows the equation x(t) = 3cos(π t) + 2. But keep in mind, this is just a silly hypothetical scenario!
To determine which of these physical settings makes sense for the object moving along the x-axis, we need to analyze the given position function x(t) = 3cos(πt) + 2.
The position function describes the motion of an object along the x-axis over time. It represents an oscillatory motion, where the object moves back and forth around a fixed point.
Now let's examine each setting:
a. A skydiver falling from a plane, before she opens her parachute.
In this scenario, the skydiver is falling in freefall, which means she experiences a constant acceleration due to gravity. However, the position function provided does not match the characteristics of freefall but rather describes an oscillatory motion. Therefore, this setting does not make sense for the given position function.
b. The shadow cast by a rock that's stuck on the edge of a spinning wheel.
For an object stuck on the edge of a spinning wheel, the shadow it casts will move in a circular motion. The position function given does not describe circular motion but rather an oscillatory motion along the x-axis. Hence, this setting does not make sense either.
c. A car driving from San Diego to Los Angeles.
Driving from one place to another usually involves linear motion along the x-axis. The given position function does not represent a straight, linear motion but rather an oscillatory motion. Consequently, this setting also does not make sense.
d. An ant walking at a steady pace from the tip of a propeller toward the hub.
In this scenario, the ant is moving in a linear motion from one point to another. The given position function describes oscillatory motion along the x-axis, not linear motion. Therefore, this setting does not make sense either.
Based on our analysis, we find that none of the settings mentioned match the characteristics of the object's motion described by the provided position function x(t) = 3cos(πt) + 2. Hence, the correct answer is e. None of these settings.