Question

A particle is projected under gravity $ (g=9.81\,\,m/{{s}^{2}}) $ with a velocity of $ 29.43\,\,m/s $ at an elevation of $ {{30}^{o}} $ . The time of flight in seconds to a height of $ 9.81\,\,m $ are

• A. $ 1,\,\,2 $
• B. $ 5,\,\,1.5 $
• C. $ 1.5,\,\,2 $
• D. $ 2,\,\,3 $

Answer 1

Answer: (A)

For the vertical motion,
$ 9.81=29.43\sin {{30}^{o}}-\frac{1}{2}\times 9.81\times {{t}^{2}} $
$ [\because $ Vertical displacement $ =(u\sin \alpha )t-\frac{1}{2}g{{t}^{2}}] $
$ \Rightarrow $ $ 1=3\sin {{30}^{o}}t-\frac{{{t}^{2}}}{2} $
$ \Rightarrow $ $ {{t}^{2}}-3t+2=0 $
$ \Rightarrow $ $ t=1,\,\,2 $