SOLUTION: Hi could you help me solve his problem. The section im working on is graphing square root and other radicals functions. The formula t=2(pi symbol)square root of (L/9.8) can b

Algebra ->  Graphs -> SOLUTION: Hi could you help me solve his problem. The section im working on is graphing square root and other radicals functions. The formula t=2(pi symbol)square root of (L/9.8) can b      Log On


   

Question 126910: Hi could you help me solve his problem. The section im working on is graphing square root and other radicals functions.
The formula t=2(pi symbol)square root of (L/9.8)
can be used to estimate the number of seconds t it takes a pendulum of length L meters to make one complete swing. Graph the equation on a graphing calculator. Then use the graph to estimate the values of t for pendulums of lengths 1.5 meters and 2.5 meters. (1 point)
Thanks :)
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
Let t (the number of seconds for 1 complete swing of the pendulum) be represented on the
vertical axis (y-axis). And let L (the length of the pendulum arm in meters) be represented
on the horizontal axis (x-axis)
.
You can easily calculate a couple of points on the graph of:
.
t+=+2%2Api%2Asqrt%28L%2F9.8%29
.
just to check what your calculator shows as the graph. First you can tell that L has to be
a positive value. Why? Because if it were negative you would be taking the square root of
a negative number and this means that the answer would not be a real number. (Also it doesn't make
sense that a pendulum would involve a negative length.)
.
What if L is zero? If you substitute zero for L in the equation, the square root term becomes zero
and this makes the whole right side of the equation become zero. So when L = 0 then t also
equals zero. This means that the point (0,0) is on the graph. Note that this is just a
mathematical solution. It really makes no sense to have a pendulum with an arm of zero length.
.
What if L is 9.8? Then the term in the radical becomes 1 and the square root is 1. This
makes the right side of the equation become:
.
t+=+2%2Api%2A1+=+2%2Api
.
and 2%2Api is approximately 6.28. So the point (L, t) is (9.8, 6.28) and it should be
on the graph.
.
These are points on the graph just to help us get a feel that our graph is correct.
.
When you do the graph on your calculator it should look like this:
.
graph%28600%2C600%2C-3%2C15%2C-3%2C10%2C2%2A3.141592654%2Asqrt%28x%2F9.8%29%29
.
Note that (0,0) is a point on the graph. And when you go to 9.8 on the horizontal
axis, the corresponding value in the vertical direction appears to be 6.28 just as we had
said. The graph appears to be correct.
.
Now all you have to do to answer the problem is:
.
First, go out to 1.5 on the horizontal axis and determine how many vertical units you have to go
up to get to the graph. (You should get an answer of about 2.458 seconds.)
.
Then go out to 2.5 on the horizontal and determine from that point how many vertical units
you have to go up to get to the graph. (You should get an answer of about 3.173 seconds.)
.
Hope this helps you to understand the problem and how to solve it.
.