PHP & XML: Access attribute of XML response with colon?

Question

My PHP curl request gets an XML response like this:

<feed>
    <openSearch:totalResults>0</openSearch:totalResults>
    <openSearch:startIndex>1</openSearch:startIndex>
    <openSearch:itemsPerPage>10</openSearch:itemsPerPage>
    <openSearch:Query role="correction" searchTerms="BINGO"/>
</feed>

After I parse it with SimpleXML_load_string() I want to access the attribute 'searchTerms' in the last openSearch:Query node. How can I get this?

I tried:

$xml = simplexml_load_string($result);
$searchTerms = $xml->openSearch->Query->searchTerms; // empty value
$searchTerms = $xml->openSearch:Query->searchTerms; // syntax error, unexpected ':'
$searchTerms = $xml->openSearch[3]->searchTerms; // empty value
$searchTerms = $xml->openSearch[3]['searchTerms']; // empty value

thank you for your assistance.