Question

An object is projected with a velocity of 10m/s at an angle 0 45 with horizontal. The equation of trajectory followed by the projectile is 2 y x x     , the ratio  / is

Answer 1

Correct Question :-

An object is projected with a velocity of 10m/s at an angle 45∘ with horizontal. The equation of trajectory followed by the projectile is y = ax − βx², the ratio α/β is ?

SoluTion :-

$\sf {y=\alpha x-\beta x^{2}=xtan\theta- \frac{gx^{2}}{2u^{2}cos^{2}\theta} }$

$\sf {\alpha=tan\ \theta,\beta=\frac{g}{2u^{2}cos^{2}\theta} }$

$\sf {\frac{\alpha }{\beta } =\frac{tan\ \theta}{g/2u^{2}cos^{2}\theta} }$

$\sf {=\frac{2u^{2}cos\ \theta sin\ \theta }{g}\ =\ \frac{2u^{2}cos^{2}\ \theta\ tan\ \theta}{g} }$

$\sf {\frac{10^{2}}{10}\ sin\ 90^{o}=10 }$