Question

A small body is thrown at an angle to the horizontal with the initial velocity ${\overrightarrow{v}}_0$. Neglecting the air drag, find the displacement of the body as a function of time $r\left(t\right)$.

• A. $\overrightarrow{r}={\overrightarrow{v}}_{0}t+\frac{\overrightarrow{g}{t}^2}{2}$
• B. $\overrightarrow{r}={\overrightarrow{v}}_{0}t-\frac{\overrightarrow{g}{t}^2}{2}$
• C. $\overrightarrow{r}=2{\overrightarrow{v}}_{0}t-\frac{\overrightarrow{g}{t}^2}{2}$
• D. $\overrightarrow{r}=2{\overrightarrow{v}}_{0}t+\frac{\overrightarrow{g}{t}^2}{2}$

Answer 1

The correct option is A $\overrightarrow{r}={\overrightarrow{v}}_{0}t+\frac{\overrightarrow{g}{t}^2}{2}$

${\overrightarrow{v}}_o=u\cos \theta \hat{i}+u\sin \theta \hat{j}$

Using, $y=u\sin \theta t+\frac{1}{2}\overrightarrow{g}{t}^2$

$x=u\cos \theta t$

so, $\overrightarrow{r}=x\hat{i}+y\hat{j}=\overrightarrow{v_o}t+\frac{1}{2}\overrightarrow{g}{t}^2$