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 $$g = 10ms^{-2}).$$

A
tan123
B
tan132
C
tan174
D
tan145

Solution

## The correct option is C $$\tan { ^{-1}\frac {7 }{ 4 } }$$t=0  x=0,y=0t=2se x=40,y=50but $$x=ux\times t\Rightarrow ux=\frac{x}{t}=\frac{40}{x}=20m$$$$\rightarrow u cos\theta =20m-----(1)$$$$y=50 but y= (u sin\theta )t-\frac{9t^{2}}{2}$$or  y$$=(u sin\theta )2\frac{-10}{2}.(4)=24since-20$$or $$so=24sin\theta -20\Rightarrow usin\theta =35----(2)$$$$\frac{usin\theta }{ucos\theta }=\frac{35}{20}=\frac{7}{4}$$$$\Rightarrow \theta =tan^{-1}\frac{7}{4}$$Physics

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