Question

A particle is projected horizontally from a building of small height with velocity $v_0$. Neglecting air friction, choose correct options about path of the projectile for different $v_0$. [M is mass of earth]

• A. Part of Ellipse for $v_0=\sqrt{\frac{GM}{2R}}$
• B. Parabolic for $v_0=\sqrt{\frac{2}{3}\frac{GM}{R}}$
• C. Circular for $v_0=\sqrt{\frac{GM}{R}}$
• D. Parabolic for $v_0=\sqrt{\frac{2GM}{R}}$

Answer 1

Answer: (A), (C), (D)

The correct options are
A Part of Ellipse for $v_0=\sqrt{\frac{GM}{2R}}$
C Circular for $v_0=\sqrt{\frac{GM}{R}}$
D Parabolic for $v_0=\sqrt{\frac{2GM}{R}}$

Total energy $E=\frac{1}{2}m{v}^2-\frac{GMm}{R}$

For E = 0, $v=\sqrt{\frac{2GM}{R}}$ Path is parabola

For E = -ve, $v<\sqrt{\frac{2GM}{R}}$ Path is elliptical

where for $v=\sqrt{\frac{GM}{R}}$ Special case of ellipse that is circle.
If $v<\sqrt{\frac{GM}{R}}$, then the elliptical part would not be completed as it will collide with earth. So path followed is part of ellipse.