Question

The acceleration of C w.r.t. ground if a = b = 1 m/s^2

Answer 1

acceleration of block C is 4.12 m/s with respect to ground.

it is given that acceleration of block A is 1 m/s² and acceleration of block B is also 1 m/s².

we have to find the acceleration of C w.r.t ground.

see figure,

displacement of C along y-axis, C = $l_1+l_2+l_3+l_4$

differentiating twice with respect to time t,

$a_C=a_1+a_2+a_3+a_4$

here $l_1$ part decreases when block C is moving downward. here acceleration of a w.r.t to b = a - (-b) = a + b.

so, $a_1=-(a+b)$

similarly, $a_3=-(a+b)$

but $a_2$ and $a_4$ doesn't change so, $a_2=a_4=0$

so, $a_C=-(a+b)+0-(a+b)+0=-2(a+b)$

now displacement of C along x - axis.

displacement of block C only depends on block A.

so, acceleration of block C along x-axis = acceleration of a = a

so, acceleration of block C = $a\hat i-2(a+b)\hat j$

now putting a = b = 1

so $a_C=1\hat i-4\hat j$

so, |$a_C$| = √(1² + 4²) = 4.12 m/s

Answer 2

Answer:

acceleration of block C is 4.12 m/s with respect to ground.