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 ( 1) is correct, i.e., options (2), (3) and (4) are incorrect.