Question

Find the velocity of block $A$ i.e. $V_A$ in the shown figure.

• A. $V_A=38\text{m/s}$, downwards
• B. $V_A=42\text{m/s}$, downwards
• C. $V_A=38\text{m/s}$, upwards
• D. $V_A=42\text{m/s}$, upwards

Answer 1

The correct option is D $V_A=42\text{m/s}$, upwards

Let the given condition be modified as shown in the below figure

Assuming, the block $A$ and pulley $P_2$ move upward and taking upward as positive, we have
For Pulley $P_2$:
$V_{P2}=\frac{V_B+V_A}{2}=\frac{4+V_A}{2}$....(i)
Now, for pulley $P_1$:
$V_{P1}=\frac{V_C+V_{P2}}{2}=\frac{-3+\frac{4+V_A}{2}}{2}$
$\Rightarrow 10=\frac{-2+V_A}{4}\Rightarrow V_A=42\text{m/s}$
Hence, the velocity of block $A$ is $V_A=42\text{m/s}$, upwards.