Question

If block A has a velocity of 0.6 m/s to the right, determine the velocity of block B.

• A. 1.8 m/s in downward direction
• B. 1.8 m/s in upward direction
• C. 0.6 m/s in downward direction
• D. 0.6 m/s in upward direction

Answer 1

Answer: (A)

1.8 m/s in downward direction

Answer 2

Let $x_A$ be the horizontal position of block A and $y_B$ be the vertical position of block B.

From the diagram, it can be observed that the length of the string can be expressed as:

$L = 3x_A + y_B + \text{constant}$

Taking the derivative with respect to time:

$0 = 3v_A + v_B$

$v_B = -3v_A$

Given that $v_A = 0.6 \text{ m/s}$ (to the right), then:

$v_B = -3(0.6) = -1.8 \text{ m/s}$

The negative sign indicates that the velocity of block B is in the opposite direction to the velocity of block A. Since block A is moving to the right, block B moves downward. Therefore, the velocity of block B is 1.8 m/s in the downward direction.