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(C) Let the acceleration of block $A$ be $a_A = 5\,m/s^2$ (horizontal).Block $B$ is constrained by the pulley system. As block $A$ moves to the right,

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$5\sqrt{5}\,m/s^2$

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(C) Let the acceleration of block $A$ be $a_A = 5\,m/s^2$ (horizontal).Block $B$ is constrained by the pulley system. As block $A$ moves to the right,the string connected to $A$ pulls block $B$ upwards.From the constraint relation,the length of the string $L = x_A + 2y_B$ is constant (where $x_A$ is the horizontal displacement of $A$ and $y_B$ is the vertical displacement of $B$).Differentiating with respect to time twice,we get $a_A = 2a_B$ (in terms of magnitude of vertical acceleration of $B$ relative to $A$).However,since $B$ is also moving horizontally with $A$,its horizontal acceleration is $a_{Bx} = 5\,m/s^2$ and its vertical acceleration is $a_{By} = 2 	imes a_A = 10\,m/s^2$.The net acceleration of $B$ with respect to the ground is $a_B = \sqrt{a_{Bx}^2 + a_{By}^2}$.$a_B = \sqrt{5^2 + 10^2} = \sqrt{25 + 100} = \sqrt{125} = 5\sqrt{5}\,m/s^2$.

If block $A$ is moving with an acceleration of $5\,m/s^2$,the acceleration of $B$ with respect to the ground is:

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