How can this English sentence be translated into a logical expression? ( Translating " unless") 
You cannot ride the roller coaster if you are under 4 feet tall unless you are older than 16 years old.

Let:


*

*$P$ stands for "you can ride the roller coaster"

*$Q$ stands for "you are under 4 feet tall"

*$R$ stands for "you are older than 16 years old"
Is this logical expression correctly translated?
$$P \rightarrow (Q \wedge R)$$
 A: The suggestion of $P\to (Q \wedge R)$ would say that in order to ride the roller coaster you must be at least $4$ feet tall and you must me at least $16$ years old.  But I would say the meaning of the given sentence is that you need to satisfy one of the age and height conditions, not both.
I think the sentence means: In order to ride the roller coaster, you must be at least $4$ feet tall, or you must be over $16$ years old.
Symbolically (using your $P, Q, R$), this would be $P\to (Q\vee R)$. In contrapositive form (which would tell you what keeps you from riding the roller coaster: $(\neg P\wedge \neg Q)\to \neg R$.  (If you are under 4 feet tall and younger than $16$, then you can't ride the roller coaster).
A: (1) 'Unless' statements:
There are some known strategies to transform 'unless' clauses into conditional statements. The most common one seems to be directly translate them using 'if not':


*

*I'm not coming to the party unless Sylvia comes.

*I wouldn't eat that food unless I was really hungry.
The examples above can be respectively translated as follows:


*

*If Sylvia is not coming to the party, neither am I.

*If am not really hungry I wouldn't eat that food.
Alternatively, we can use their (reverse) contrapositive forms:


*

*I am coming to the party if Sylvia is.

*I would eat that food If was really hungry.
(2) Your Answer:
Consider the English sentence

You cannot ride the roller coaster if you are under 4 feet tall unless you are older than 16 years old.

Following the above reasoning we have:

If you are not older than 16 years, then you cannot ride the roller coaster if you are under 4 feet tall.

which is the same as:

If you are not older than 16 years, then if you are under 4 feet tall you cannot ride the roller coaster.

Now let: 


*

*$P$ stand for 'you can ride the roller coaster'

*$Q$ stand for 'you are under 4 feet tall'

*$R$ stand for 'you are older than 16 years old'


The answer you are looking for is
$$ \neg R \to (Q \to \neg P).$$
A: Solution: let suppose 
q= You can ride the roller coaster;
p= you are older than 16 years old;
r= you are under 4 feet tall;
There is two states of “q if p” and “q if r”;
Because 
•   q unless p :: (the statement is as )
You can ride the roller coaster unless you are not older than 16 years old;
•   q, if r :: (the statement is as)
You can ride the roller coaster unless you are under 4 feet tall;
•   These two statements have same conclusion that is “you can ride a roller coaster” and the hypothesis are two.
So these two conclusions may be simplify in one statement as:
“You can ride the roller coaster, if you are under 4 feet tall and you are not older than 16 years old”
Then in this statement there is the (q, if p) form of implication and p which is the hypothesis has the operator “and” .So, the expression is 
Hypothesis -> conclusion as:
                (r ^ ~p) -> ~q
Where ~p means: you are not older than 16 years old” and 
~q means: You cannot ride the roller coaster.
A: No, because $P\implies Q\land R$ actually means that You must be under 4 feet tall and older than 16 to ride the roller coaster which is not true. You can be under 4 feet tall and more than 16 years old and still ride the roller coaster. The sentence of the question is equivalent to:

If you are more than 16 years old or more than 4 feet tall or both, you can ride the roller coaster.

which is $$(\lnot Q\lor R)\implies P$$so, the if-else-then statements always work.
Another way to tackle these sort of problem is the truth table:
$$
\begin{matrix}
Q&R&P
\\0&0&1
\\0&1&1
\\1&0&0
\\1&1&1
\end{matrix}
$$
