Question

A particle is moving under the influence of a force which is fixed in magnitude and acting at an angle $\theta$ in the direction of motion. The path described by the particle is

• A. a circle
• B. an ellipse
• C. a parabola
• D. a straight line

Answer 1

Answer: (C)

a parabola

Answer 2

Let a body be projected up with an initial velocity $u$, inclined at an angle $\theta$ with the horizontal, then the velocity in horizontal and vertical motion is
$u_{x} =u \cos \theta,$
$u_{y} =u \sin \theta$

The body moves under constant gravitational acceleration $g$, acting vertically downward. Therefore, horizontal velocity remains constant but vertical velocity changes. The equation of trajectory is
$y=x \tan \theta-\frac{1}{2} \frac{g}{u^{2} \cos ^{2} \theta} x^{2}$
This equation is quadratic in $x$ and linear in $y$, therefore it represents a parabola.