3 meter,
Find the speed of the jet plane
( 3 = 1.732)
30o
3600
3
m
3600
3
m
60o
Height of the person is neglected
P
Q
R
S
A
line of sight
line of sight
Horizontal line
Q. The angle of elevation of a jet plane from a point A on the ground is 60o.
After a flight of 30 seconds, the angle of elevation changes to 30o.
If the jet plane is flying at a constant height of 3600
Speed =
Distance
Time
3 m
3 meter,
Find the speed of the jet plane
Q. The angle of elevation of a jet plane from a point A on the ground is 60o.
After a flight of 30 seconds, the angle of elevation changes to 30o.
If the jet plane is flying at a constant height of 3600
Let P and Q be the first and second position
of a jet plane.
A represents the point on the ground.
∠PAS and ∠QAR are the angles of elevation.
∠PAS = 60o,
PS and QR represents constant height at
which the jet plane is flying.
PS = QR = 3600
In right angled ΔPSA,
tan 60o =
PS
AS
3
=
AS
3600
3
3
=
AS
3600
3
AS =
3600 m
tan 60o =
?
Sol.
( 3 = 1.732)
Observe ∠A
For ∠PAS
Opposite side →
Adjacent side →
PS
AS
Ratio of opposite side and Adjacent side reminds us of _________
‘tan’
SR is part of AR
AS + SR = AR
∴ SR = AR – AS
AS belongs to ΔPSA
∠QAR = 30o
A
P
Q
S
R
60o
3600
3
m
3600
3
m
30o
Adjacent side
Opposite
side
Speed =
Distance
Time
PQ or SR
?
?
SR = AR – AS
2nd position
1st position
∴
∴
∴
3600 m
3600 m
10800 m
Q. The angle of elevation of a jet plane from a point A on the ground is 60o.
After a flight of 30 seconds, the angle of elevation changes to 30o.
If the jet plane is flying at a constant height of 3600
Find the speed of the jet plane.
3 meter,
A
P
Q
S
R
60o
3600
3
m
3600
3
m
30o
In right angled ΔQRA,
tan 30o
QR
AR
3
1
=
AR
3600
3
∴
∴
AR
=
3600
3
3
x
∴
AR
10800 m
=
=
AS
+
SR
=
AR
∴
3600
+
SR
=
10800
∴
SR
=
10800
–
3600
∴
SR
=
7200 m
□PQRS is a rectangle.
PQ
=
SR
=
7200m
Distance covered
in 30 sec. =
7200m
Speed =
Distance
Time
PQ
30 sec.
=
Adjacent side
Opposite
side
tan 30o =
?
1
AS =
3600 m
7200m
7200m
( 3 = 1.732)
Observe ∠QAR
For ∠QAR
Opposite side →
Adjacent side →
QR
AR
Ratio of opposite side and Adjacent side reminds us of _________
‘tan’
Sol.
AR is made up of
AS and SR
SR = AR – AS
AR belongs ΔQRA
∴
AR
=
3600
× 3
3 meter,
3 = 1.732 )
(
Speed
PQ
30 sec.
=
7200 m
30 sec.
=
7200
1000
=
30
3600
÷
7200
1000
=
3600
30
x
=
864
km/hr.
The speed of the jet plane is 864 km/hr.
3 meter,
1 km = 1000 m
1 hr. = 3600 sec.
A
P
Q
S
R
60o
3600
3
m
3600
3
m
30o
120
=
72 × 12
km/hr.
Q. The angle of elevation of a jet plane from a point A on the ground is 60o.
After a flight of 30 seconds, the angle of elevation changes to 30o.
If the jet plane is flying at a constant height of 3600
Find the speed of the jet plane.
Sol.
10800 m
7200m
7200m
3600 m