Question

Sol. [Key Concept: Displacement $s = \frac{1}{2}\ a\ t^{2}$ with $a = F/m$; take the ratio of its two components.]

$${\overrightarrow{a} = \frac{\overrightarrow{F}}{m} = \frac{5\widehat{i} + 10\widehat{j}}{0.1} = (50\widehat{i} + 100\widehat{j}) }{\overrightarrow{s} = \overrightarrow{u}t + \frac{1}{2}\overrightarrow{a}t^{2} }{\overrightarrow{s} = 0 + \frac{1}{2}\lbrack 50\widehat{i} + 100\widehat{j}\rbrack\lbrack 2\rbrack^{2} }{\overrightarrow{s} = 100\widehat{i} + 200\widehat{j} = \overrightarrow{r} = 2x\widehat{i} + 5y\widehat{j} }{2x = 100\ 5y = 200}$$

$$\frac{x}{y} = \frac{5}{4} $$