A ship is at a distance of 560 m from a fort defending the harbour entrance of an island - Physics - Sources of Energy

Question

A ship is at a distance of 560 m from a fort defending the harbour
entrance of an island A defence cannon, located at sea level, fires
balls at initial speed u 82 m/s
(a) At what angle 0 from the horizontal, must a ball be fired to
hit the ship?

(b) How far should the ship be from the cannon, if it is to be
beyond the maximum range of the cannon balls?

Rohit Babu · Accepted Answer

Dear Student,Given,R=560m, u=82m/si)The horizontal range is,R=u2sin2θg⇒560=82×82×sin2θ9
8=686 14×sin2θ⇒sin2θ=560686 14=0
816⇒2θ=sin-10 816=54 700⇒θ=27
350Ball must be fired at an angle θ=27
350ii)The maximum range of the cannon ball will be when θ=450⇒Rcannon=u2sin2θg=82×82×sin9009
8=686
12mAt this range the cannon ball will hit the ship
So the ship should be at a distance >686
12mRegards