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3-2.Motion in Plane
hard
A projectile is thrown with a velocity of $50\,\, ms^{^{-1}}$ at an angle of $53^o$ with the horizontal Determine the instants at which the projectile is at the same height
A$t = 1\,\,s$ and $t = 7s\,\,$
B$t = 3\,\,s$ and $t = 5\,\,s$
C$t = 2\,\,s$ and $t = 6\,\, s$
Dall the above
Solution
$y=u_y t+\frac{1}{2} a_y t^2 \Rightarrow y=u_y t-\frac{1}{2} g t^2$
$g t^2-2 u_y+2 h=0 \Rightarrow t=\frac{2 u_y \pm \sqrt{4 u_y^2-8 g h}}{2 g}$
$t_1=(u_y+\sqrt{u_y^2-2gh}/g, t_2 =(u_y-\sqrt{u_y^2-2gh}/g$
$t_1 +t_2 =(2u_y)/(g) = (2 \times 50 \times sin 53^o)/(10) = 8sec.$
$g t^2-2 u_y+2 h=0 \Rightarrow t=\frac{2 u_y \pm \sqrt{4 u_y^2-8 g h}}{2 g}$
$t_1=(u_y+\sqrt{u_y^2-2gh}/g, t_2 =(u_y-\sqrt{u_y^2-2gh}/g$
$t_1 +t_2 =(2u_y)/(g) = (2 \times 50 \times sin 53^o)/(10) = 8sec.$
Standard 11
Physics
