AP EAMCET Engineering 2018 Apr 22 Shift 1 Paper

Consider the figure shown below.Let the velocity of the projectile at an angle

θ

2

be v. The velocity of the projectile in the horizontal direction remains same throughout the motion.
v‌cos‌ ‌

θ

2

=u‌cos‌θ
v=

u‌cos‌θ

cos‌ θ 2

The component of force perpendicular to the direction of motion provides the required centripetal force.

mv2

r

=mg‌cos‌

θ

2

r=

v2

g‌cos‌ θ 2

Substituting the value of v in above expression, we get
r=

( u‌cos‌θ cos‌ θ 2 )2

g‌cos‌ θ 2

=

u2cos2θ.sec3( θ 2 )

g