A body is projected at angle 2ϴ,what is another angle of projection for same range?
Answers
11th
Physics
Motion in a Plane
Projectile Motion
A projectile can have the s...
PHYSICS
A projectile can have the same range for two angles of projection. If h
1
and h
2
are maximum heights when the range in the two cases is R, then the relation between R, h
1
and h
2
is
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ANSWER
h
1
=
2g
u
2
sin
2
θ
h
2
=
2g
u
2
sin
2
θ(90−θ)
,R=
g
u
2
sin
2
θ
Range R is same for angle θ and (90
o
−θ)
∴h
1
h
2
=
2g
u
2
sin
2
θ
×
2g
u
2
sin
2
θ(90−θ)
=
4g
2
u
4
(sin
2
θ)×sin
2
(90−θ)
[∵sin(90−θ)=cosθ]
=
4g
2
u
4
(sin
2
θ)×cos
2
θ
[∵sin
2
θ=2sinθcosθ]
=
4g
2
u
4
(sinθcosθ)
2
=
16g
2
u
4
(sin
2
θ)
2
=
16g
2
u
4
(sinθcosθ)
2
=
16
R
2
or, R
2
=16h
1
h
2
orR=4
h
1
h
2
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