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3-2.Motion in Plane
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The equation of motion of a projectile is $y = Ax -Bx^2$ where $A$ and $B$ are the constants of motion. The horizontal range of the projectile is
A$\frac{A}{B}$
B$\frac{B}{A}$
C$\frac{A^2}{B}$
D$\frac{B^2}{A}$
Solution
$\because \quad \mathrm{y}=\mathrm{Ax}-\mathrm{Bx}^{2}$
at $\quad x=R, y=0$
and $x=0, y=0$
so put $y=0$
${\mathrm{Ax}-\mathrm{Bx}^{2}=0}$
${\mathrm{x}(\mathrm{A}-\mathrm{Bx})=0}$
$x=0$ or $A-B x=0$
for $x=0,$ initial point
and $A-B x=0 \rightarrow x=\frac{A B}{B}$ or $R=\frac{A}{B}$
at $\quad x=R, y=0$
and $x=0, y=0$
so put $y=0$
${\mathrm{Ax}-\mathrm{Bx}^{2}=0}$
${\mathrm{x}(\mathrm{A}-\mathrm{Bx})=0}$
$x=0$ or $A-B x=0$
for $x=0,$ initial point
and $A-B x=0 \rightarrow x=\frac{A B}{B}$ or $R=\frac{A}{B}$
Standard 11
Physics
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