Question

A fly starts out 2 meters from a lightbulb, flies closer to the light, then farther away (2 meters again). At this point the fly goes toward the bulb again, but hits the bulb and then finally flies away.
Find a function (it may be piecewise) that gives the distance of the bug from the light as a function of time. [There is more than one solution hereâyou have lots of freedom with what your function can be, but it must satisfy the situational requirements given.] Demonstrate that your function DOES satisfy the situational requirements.

What is the domain and range of your function for this situation?

Answer 1

Answer

f(t)=2cos(t)

Step-by-step explanation:

let's describe the situation first, a fly is starting 2 meters from the bulb and flies towards the bulb and when it is really close to the bulb, it flies 2 meters further away from the bulb this means that it reaches d = 0m (distance from the bulb) and then flies further 2 meters so d = -2m.

it this point the fly returns back and touches the bulb and flies away (ends it's oscillatory motion ). d = 0 again and story ends here.

here if we want to model this problem with time function , the cosine function seems the best fit with amplitude of 2, so the answer is f(t) = 2cos(t).

Now you can ask why cosine function? well if you look at the graph or the plot of the function it perfectly captures the physical situation going on here in this problem.

Domain is 0 to 2$\pi$ because it is one complete cycle and the range is -2 to +2.