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
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B
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C
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D
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Solution
The correct option is D If the particle is projected with velocity u at angle θ, then equation of its trajectory will be: y=xtanθ−gx22u2cos2θ
We know slope is given by m=dydx
Therefore, slope m=tanθ−gxu2cos2θ
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.