A stone projected from ground with certain speed at an angle #alpha#with horizontal attains maximum height #h_1#when it is projected with same speed at an angle#alpha# with vertical attains height #h_2#.What is the horizontal range of projectile?
1 Answer
Deduction of formulas
Let the velocity of projection of the stone be u with angle of projection
The vertical component of the velocity of projection is
Now if the time of flight be T then the object will return to the ground after T sec and during this T sec its total vertical displacement h will be zero. So applying the equation of motion under gravity we can write
The horizontal displacement or range during this T sec is
If H be the maximum height attained by the stone we can write
CALCULATION USING ABOVE RELATIONS
For 1st case
when
So horizontal range
and
For 2nd case
when
So horizontal range
and
In both the cases the range is same.So let
Hence range
Now multiplying [4] and [6] we get