Question

Five forces ${\vec{F}}_1,{\vec{F}}_2,{\vec{F}}_3,{\vec{F}}_4$ and ${\vec{F}}_5$ are acting on a particle of mass $2.0kg$ so that it is moving with $4m/s^2$ in east direction. If ${\vec{F}}_1$ force is removed, then the acceleration becomes $7m/s^2$ 2 in north, then the acceleration of the block if only ${\vec{F}}_1$ is acting will be $\sqrt{n}m/s^2$ Find the value of n

Answer 1

Answer: 65

${\vec{F}}_1+{\vec{F}}_2+{\vec{F}}_3+{\vec{F}}_4+{\vec{F}}_5=2\left(4i\right)\dots \left(i\right)$
and ${\vec{F}}_2+{\vec{F}}_3+{\vec{F}}_4+{\vec{F}}_5=2\left(7j\right)\dots \left(ii\right)$
From $\left(i\right)$ and $\left(ii\right)$, ${\vec{F}}_1=8\hat{i}-14\hat{j}$
${\vec{a}}_1=\frac{{\vec{F}}_1}{m}=4\hat{i}-7\hat{j}$
$\Rightarrow a_1=\sqrt{16+49}=\sqrt{65}m/s^2$