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 of the particle varies not according to which of the following curves?

• A.
• B.
• C.
• D.

Answer 1

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

If the particle is projected with velocity u at angle $\theta$, then equation of its trajectory will be:
$y=xtan\theta -\frac{g{x}^2}{2u^{2}co{s}^2\theta }$
We know slope is given by $m=\frac{dy}{dx}$
Therefore, slope $m=\text{tan}\theta -\frac{gx}{u^{2}co{s}^2\theta }$
It implies that the graph between slope and $x$ will be straight line having negative slope and a non- zero positive intercept on y - axis.
But $x$ is directly proportional to the time t, therefore, the shape of graph between slope and time will be same as that of the graph between slope and $x$. Hence, only option (a) is correct, i.e., options (b), (c), and (d) are incorrect.