Question

The two ends A and B of a uniform rod of length $\ell =1m$ are moving with velocities $V_A$ and $V_B$ as shown.The velocity $V_B$ is:

• A. 25 m/s
• B. 15 m/s
• C. 20 m/s
• D. 50 m/s

Answer 1

The correct option is B 15 m/s

Given that,

Velocity of $A=20$ m/s

Velocity of $B=V_B$ m/s

According to diagram

Velocity of $A$ along $X$ axis towards $B$ is

$V_{AX}=V_A\cos {53}^0$

$V_{AX}=20\cos {53}^0$

$V_{AX}=20\times \frac{3}{5}$

$V_{AX}=12m/s....\left(I\right)$

Now, velocity of $B$ along $X$ axis towards $A$ is

$V_{BX}=V_B\cos {37}^0$

$V_{BX}=V_B\times \frac{3.95}{5}$

$V_{BX}=V_B\times \frac{4}{5}....\left(II\right)$

Now, from equation (I) and (II)

$12=V_B\times \frac{4}{5}$

$V_B=\frac{60}{4}$

$V_B=15m/s$

Hence, the velocity $V_B$ is $15$ m/s