Question

A heavy particle is projected with a velocity at an angle with the horizontal into the uniform gravitational field. The slope of the trajectory of the particle varies as
A. .
B. .
C. .
D. .

Answer 1

Correct Answer - B::C::D
(b.,c.,d.) If the particle is projected with velocity `u` at an angle `theta`, then equation of its trajectory will be
`y = x tan theta -(gx^2)/(2 u^2 cos^2 theta)`
We know slope is given by `m = (dy)/(dx)`
Therefore, slope `m = tan theta - (gx)/(u^2 cos^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.