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?

If the particle is projected with velocity u at an angle θ then equation of its trajectory will bey=xtan⁡θ−gx22u2cos2⁡θWe know slope is given by m=dydxTherefore, slope m=tan⁡θ−gxu2cos2⁡θIt 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.