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A heavy particle is projected with a vel...

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

.

Text Solution

Verified by Experts

The correct Answer is:
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.
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