A) The vertical component of velocity v is taking the rock to a height
Vertical component =
The time taken to reach maximum height =
So total time of rocks flight =
Range of rock is due to the horizontal component of velocity =
Range =
=
Maximum height =
=
Since range = maximum height
We have
So when angle of projection is
range is equal to maximum height reached.
b) We have range =
=
Maximum of range is reached when
Maximum range =
c) For range to be equal to maximum height only condition is
, it does not depend upon acceleration due to gravity and velocity. That angle is a constant.