Two transparent elevator cars $A$ and $B$ are moving in front of each other. Car $A$ is moving up and retarding at ${a_2}$. Person in the car $A$ drops a coin inside the car. What is the acceleration by person in car $B$.
A) $g + {a_2}$ download
B) $g - {a_1} - {a_2}$ download
C) $g - {a_1} + {a_2}$ download
D) none of the above

Hint: This sum is completely based on the understandable assumptions. Find the acceleration of the coin that falls from the elevator $A$ into the elevator $B$ , and also the acceleration of the elevator $B$ alone. Add both of the acceleration to get the total acceleration in $B$.

Complete step by step solution:
It is given that
The car $A$ is moving upward
The car $B$ is moving downward with the retarding velocity ${a_2}$
It is also given that the coin from the car $A$ elevator falls on a car $B$ elevator. Since the car $A$ elevator is moving upward and the car $B$ elevator is moving downward, the coin falls with the acceleration due to gravity.
${a_c} = g$
In the same way, the car $B$ elevator is also moving downward with some retarding velocity. Hence its acceleration is also due to the acceleration due to gravity. But the retardation is provided in the opposite direction to that of the gravity.
$\Rightarrow {a_B} = - {a_2}$
Since the coin falls on $B$ , the total acceleration in $B$ is
$\Rightarrow a = {a_c} + {a_B}$
Substituting the known values, we get
$\Rightarrow a = g + {a_2}$
Hence it is clear that the elevator car $B$ has downward acceleration.

Thus the option (A) is correct.

Note: If the acceleration that causes the slowdowns or retards the motion is called retardation. In the elevator cars, the downward motion is not allowed free fall due to gravity, because this may cause an accident. So some of the retardation is provided.