Question

When block C is in position xC = 0.8 m, its speed is 1.5 m/s to the right. Find the velocity of block A at this instant. Note that the rope runs around the pulley B and a pin attached to block C, as indicated.

Answer 1

The answer is "2 m/s".

Step-by-step explanation:

The triangle from of the right angle:

`\to (x_c-0.8)+(1.5+y_4) +√(x_c^2 + 1.5^2)= constant`

Differentiating the above equation:

`\to V_c +V_A+ (X_cV_c)/(√(x_c^2 +1))=0\\\\\to 1-V_A+ (0.8 * 1.5)/(√( 0.8^2+1.5))=0\\\\`

`\to V_A= (1.2)/(√( 0.64+1.5))+1\\\\`

`= (1.2)/( 1.46)+1\\\\= (1.2+ 1.46)/( 1.46)\\\\ = (2.66)/(1.46)\\\\= 1.82 \ (m)/(s)\\\\= 2 \ (m)/(s)`