for two angles of projection, range (R)is same and maximum vertical heightsare different (H1,H2). find relation between H1,H2 and R
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Answered by
1
here relationship between maximum height and range is H=4R
Answered by
0
The correct option is A
R
=
4
√
h
1
h
2
For angle of projection
θ
range is
R
, hence maximum height attained corresponding to this angle:
h
1
=
u
2
sin
2
θ
2
g
Range
R
is same for angle of projection
θ
and
(
90
∘
−
θ
)
from horizontal, so maximum height for
(
90
∘
−
θ
)
angle of projection is :
⇒
h
2
=
u
2
sin
2
(
90
−
θ
)
2
g
and
R
=
u
2
sin
2
θ
g
∴
h
1
h
2
=
u
2
sin
2
θ
2
g
×
u
2
sin
2
(
90
−
θ
)
2
g
=
u
4
(
sin
2
θ
)
×
sin
2
(
90
−
θ
)
4
g
2
[
∵
sin
(
90
−
θ
)
=
cos
θ
]
⇒
h
1
h
2
=
u
4
(
sin
2
θ
)
×
cos
2
θ
4
g
2
[
∵
sin
2
θ
=
2
sin
θ
cos
θ
]
⇒
h
1
h
2
=
u
4
(
sin
θ
cos
θ
)
2
4
g
2
=
u
4
(
sin
2
θ
)
2
16
g
2
h
1
h
2
=
(
u
2
sin
2
θ
)
2
16
g
2
=
R
2
16
R
2
=
16
h
1
h
2
∴
R
=
4
√
h
1
h
2
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