Question

The position of a projectile launched from the origin at $t=o$ is given by $\overrightarrow{r}$ =$(40\hat{i}+50\hat{i})$ m at $t=2s$. If the projectile was launched at an angle $\theta$ is (Take $g=10m{s}^{-2}).$

• A. $\tan {}^{-1}\frac{2}{3}$
• B. $\tan {}^{-1}\frac{3}{2}$
• C. $\tan {}^{-1}\frac{7}{4}$
• D. $\tan {}^{-1}\frac{4}{5}$

Answer 1

The correct option is C $\tan {}^{-1}\frac{7}{4}$

t=0 x=0,y=0

t=2se x=40,y=50

but $x=ux\times t\Rightarrow ux=\frac{x}{t}=\frac{40}{x}=20m$

$\to ucos\theta =20m-----\left(1\right)$

$y=50buty=\left(usin\theta \right)t-\frac{9t^2}{2}$

or y$=\left(usin\theta \right)2\frac{-10}{2}.\left(4\right)=24since-20$

or $so=24sin\theta -20\Rightarrow usin\theta =35----\left(2\right)$

$\frac{usin\theta }{ucos\theta }=\frac{35}{20}=\frac{7}{4}$

$\Rightarrow \theta =ta{n}^{-1}\frac{7}{4}$