A vertical pole has a red mark at some height A stone is projected form a fixed point on - Physics - Motion In A Straight Line

Question

A vertical pole has a red mark at some height A stone is projected
form a fixed point on the ground When projected at an angle of 45
degree it hits the pole orthogonally 1 m above the mark When
projected at an angle with a different speed at an angle of
tan-1 (3/4), it hits the pole orthogonally 1 5 m below
the mark Find the speed and angle of projection so that it hits the
mark orthogonally to the pole (g = 10 m/s2)

Dinesh Pandey · Accepted Answer

Dear Student,

The stone hits the pole perpendicularly means that the stone was at
highest point of trajectory when angle of
projection=45°2D=Range2D=u12sin2θg2D=u12sin90°g=u12g
(1)H+1=Maximum heightH+1=u12sin245°2g=u124g (2)from (1) &
(2),2(H+1)=D (3)when angle of
projection=tan-134=37°2D=Range2D=u22sin2θ°g=2u22sin37°cos37°g
(4)H-1 5=Maximum hH-1 5=u22sin237°2g (5)from (4) &
(5),9D=24H-36 (6)from (3) & (6), we have,H=9m and D=20 mHence,
maximum height=9 mRange=2×20=40
m2D=u2sin2θg40=2u2sinθcosθg
(7)H=u2sin2θ2g9=u2sinθ sinθ2g (8)from (7) &
(8),2u2sinθcosθ40=u2sinθ
sinθ18tanθ=1820θ=tan-1910=42°substitute the
value of θ in equation
(7),40=u2sin2×42°gu2=40×10sin84°=4000 99u=4000
99=200 99=20 20 m/s