A shell is fired from a point O at an angle of 60^(@) with a speed of 40 m//s & strikes a horizontal plane throught O, at a point A. The gun is fired a second time with the same angle of elevation but a different speed v. If it hits the target which starts to rise vertically from A with a constant speed 9sqrt(3) m//s at the same instant as the shell is fired, find v.

A shell is fired from a point O at an angle of 60^(@) with a speed of

1.	A shell is fired from a point O at an angle of 60^(@) with a speed of 40 m//s & strikes a horizontal plane throught O, at a point A. The gun is fired a second time with the same angle of elevation but a different speed v. If it hits the target which starts to rise vertically from A with a constant speed 9sqrt(3) m//s at the same instant as the shell is fired, find v.
Answer» SOLUTION :RANGE `(OA)=(u^(2) sin 2 theta)/(g)=(1600 xx sqrt(3))/(10 xx 2)=80 sqrt(3)` `h = 80 sqrt(3) xx tan 60^(@) = (10 xx 80 xx 80 xx 3)/(2 xx v^(2) COS 60^(@))` Time to strike `rArr v cos60^(@) xx t = 80 sqrt(3)` `rArr t =(80 sqrt(3) xx2)/(v xx1) =(10 sqrt(3))/(v)` `h=9 sqrt(3) xx (160 sqrt(3))/(v) (480 xx 9)/(v) = (240^(2) - 38400)/(v^(2))` `v^(2) -1600 - 18V =0` `v =(18 PM sqrt(324)+6400)/(2)` `rArr v =50 m//s`.