Height of auditorium is 30 m and ball just reaches to this height so this is the maximum height of projectile. Let angle of projection is θ. ‌‌ So, ‌Hmax=30=‌
u2sin‌2θ
2g
‌‌‌‌‌30‌=‌
(30)2sin‌2θ
2×10
sin‌2θ‌=‌
600
900
=‌
2
3
‌⇒sin‌θ=√‌
2
3
‌‌ and ‌cos‌θ=‌
1
√3
Now, length of auditorium will be equal to range of projectile. ‌ So, ‌‌R=‌