Question

Five persons $A,B,C,D$ and $E$ are pulling a cart of mass $100kg$ on a smooth surface and cart is moving with acceleration $3m/s^2$ in east direction. When person 𝐴 stops pulling, it moves with acceleration $1m/s^2$ in the west direction. When person $B$ stops pulling, it moves with acceleration $24m/s^2$ in the north direction. The magnitude of acceleration (in $m/s^2$) of the cart when only $A$ and $B$ pull the cart keeping their directions same as the old directions, is:

Answer 1

When all are pulling
${\overrightarrow{F}}_{net}=100\times 3\hat{i}\dots \left(i\right)$
when $A$ stops
${\overrightarrow{F}}_{net}-{\overrightarrow{F}}_A=100\times 1(-\hat{i})\dots \left(ii\right)$
when $B$ stops
${\overrightarrow{F}}_{net}-{\overrightarrow{F}}_B=100\times 24\hat{j}\dots \left(iii\right)$
from these three get
${\overrightarrow{F}}_A+{\overrightarrow{F}}_B=(700\hat{i}-2400\hat{j})N$
hence acceleration of the cart
$\overrightarrow{a}=\frac{{\overrightarrow{F}}_A+{\overrightarrow{F}}_B}{m}=\frac{(700\hat{i}-2400\hat{j})}{100}m/s^2$
$\overrightarrow{a}=\frac{(7\hat{i}-24\hat{j})m}{s^2}$
$|\overrightarrow{a}|=\sqrt{7^2+{24}^2}=25m/s^2$
Final Answer: $25$