# Intersection point

**URL:** <https://community.wolfram.com/t/intersection-point/16630>\
**Category:** Questions\
**Tags:** algebra, equation-solving\
**Created:** [August 27, 2020, 1:52am UTC](https://community.wolfram.com/t/intersection-point/16630 "2020-08-27T01:52:36Z")\
**Posts on this page:** 2\
**Page:** 1

<div class="post-metadata">

**Author:** ![luiarboleda](https://yyz1.discourse-cdn.com/wolfram/user_avatar/community.wolfram.com/luiarboleda/32/36674_2.png) [@luiarboleda](https://community.wolfram.com/u/luiarboleda)\
**Post date:** [August 27, 2020, 1:52am UTC](https://community.wolfram.com/t/intersection-point/16630/1 "2020-08-27T01:52:36Z")

</div>

Hi,

I was trying to do a program with units.  
I want to find the intersection point of two functions

```
cau=Quantity[Range[.1,1,.2],"Meters"^3/"Seconds"];
h=Quantity[{100,90,78,64,46},"Meters"];
hs=Quantity[{50,60,72,86,108},"Meters"];

fh=Interpolation[Transpose[{cau,h}]]; (*function 1*)
fhs=Interpolation[Transpose[{cau,hs}]]; (*function 2*)

cau1=cau1/.FindRoot[fh[cau1]==fhs[cau1],{cau1,.1}]

```

Is it possible?

---

<div class="post-metadata">

**Author:** ![gianlucagorni](https://avatars.discourse-cdn.com/v4/letter/g/ec9cab/32.png) [@gianlucagorni](https://community.wolfram.com/u/gianlucagorni)\
**Post date:** [August 27, 2020, 9:43am UTC](https://community.wolfram.com/t/intersection-point/16630/2 "2020-08-27T09:43:50Z")

</div>

Just my guess: `Interpolation` and `InterpolatingPolynomial` are not (yet?) compatible with physical units. The documentation for `QuantityVariable` shows an example of `DSolve` with units:

```
DSolve[{Derivative[1][QuantityVariable[x, "Length"]][
    QuantityVariable[t, "Time"]] == 
      Quantity[5, "Meters"/"Seconds"]}, 
 QuantityVariable[x, "Length"][
    QuantityVariable[t, "Time"]], QuantityVariable[t, "Time"]]

```

but the equivalent for `NDSolve` does not work, at least with the following syntax:

```
NDSolve[{Derivative[1][QuantityVariable[x, "Length"]][
    QuantityVariable[t, "Time"]] == 
      Quantity[5, "Meters"/"Seconds"]}, 
 QuantityVariable[x, "Length"][
    QuantityVariable[t, "Time"]], {QuantityVariable[t, "Time"], 
  Quantity[0, "Seconds"], Quantity[10, "Seconds"]}]

```