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 $=(u\sin \alpha )t-\frac{1}{2}g{{t}^{2}}]$
$\Rightarrow$ $1=3\sin {{30}^{o}}t-\frac{{{t}^{2}}}{2}$
$\Rightarrow$ ${{t}^{2}}-3t+2=0$
$\Rightarrow$ $t=1,\,\,2$