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?
$$P \rightarrow (Q \wedge R)$$

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).
