Question

A heavy particle is projected with a velocity at an angle with the horizontal into a uniform gravitational field. The slope of the trajectory cannot be represented by which of the following curves?

• A.
• B.
• C.
• D.

Answer 1

Answer: (B), (C), (D)

If the particle is projected with velcoity $u$ at angle $\theta$, then equation of its trajectory will be
$y=x\tan \theta -\frac{g{x}^2}{2u^2{\cos }^2\theta }$
We know slope is given by $m=\frac{dy}{dx}$
Therefore, slope
$m=\tan \theta -\frac{gx}{u^2{\cos }^2\theta }$
So, the graph of slope vs $x$ will be straight line having negative slope and a non - zero positive intercept on y - axis.
So $b,c$ are correct options.
As $x=u\cos \theta t$, the shape of graph between slope and time will also be a straight line with negative slope and positive intercept on $y-$axis.
option (d) is also correct choice.