Question

The path followed by a body projected along y-axis is given as by $y = \sqrt{3}x - (1/2)x^{2}$, if g = 10 m/s, then the initial velocity of projectile will be – (x and y are in m)

• A. $3\sqrt{10}m ⥂ / ⥂ s$
• B. $\mathbf{2}\sqrt{\mathbf{10}}\mathbf{m}\mathbf{⥂}\mathbf{/}\mathbf{⥂}\mathbf{s}$
• C. $10\sqrt{3}m ⥂ / ⥂ s$
• D. $10\sqrt{2}m ⥂ / ⥂ s$

Answer 1

Answer: (B)

$\mathbf{2}\sqrt{\mathbf{10}}\mathbf{m}\mathbf{⥂}\mathbf{/}\mathbf{⥂}\mathbf{s}$

Answer 2

By comparing the coefficient of x² in given equation with standard equation $y = x\tan\theta - \frac{gx^{2}}{2u^{2}\cos^{2}\theta}.$ $\frac{g}{2u^{2}\cos^{2}\theta} = \frac{1}{2}$

Substituting $\theta$ = 60⁰ we get $u = 2\sqrt{10}m/\sec$.