question_answer

A particle is moving under the influence of a force which is fixed in magnitude and acting at an angle 9 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

Correct Answer: C

Solution :

                 Let a body be projected up with an initial velocity u, inclined at an angle 0 with the horizontal, then the velocity in horizontal and vertical motion is                 \[{{u}_{x}}=u\cos \theta \],                 \[{{u}_{y}}=u\cos \theta \] 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.