Question

A plane flies horizontally at an altitude of 6 km and passes directly over a tracking telescope on the ground. When the angle of elevation is π/4, this angle is decreasing at a rate of π/4 rad/min. How fast is the plane traveling at that time?

Answer #1

At a given moment, a plane passes directly above a radar station
at an altitude of 6 km and the plane's speed is 800 km/h. Let θ be
the angle that the line through the radar station and the plane
makes with the horizontal. How fast is θ changing 24 min after the
plane passes over the radar station?

An airplane flies at an altitude of y = 4
miles toward a point directly over an observer. The speed of the
plane is 500 miles per hour. Find the rates at which the angle of
elevation θ is changing when the angle is θ =
45°, θ = 60°, and θ = 70°.

A plane flying with a
constant speed of 14 km/min passes over a ground radar station at
an altitude of 11 km and climbs at an angle of 35 degrees. At what
rate is the distance from the plane to the radar station increasing
4 minutes later?
The distance is increasing at ________________________
km/min.
Hint: The law of cosines for a triangle is
c2=a2+b2−2abcos(θ)
where θ
is the angle between the sides of length a and b.

A plane flying with a constant speed of 9 km/min passes over a
ground radar station at an altitude of 6 km and climbs at an angle
of 25 degrees. At what rate is the distance from the plane to the
radar station increasing 5 minutes later?
Hint: The law of cosines for a triangle is
c^2=(a^2)+(b^2)−2abcos(θ)
where ? is the angle between the sides of length a and b

A plane flying horizontally at an altitude of 1 mi and a speed
of 480 mi/h passes directly over a radar station. Find the rate at
which the distance from the plane to the station is increasing when
it is 4 mi away from the station. (Round your answer to the nearest
whole number.)

1.A conical tank has height 3 m and radius 2 m at the top. Water
flows in at a rate of 1.5 m3/min. How fast is the water
level rising when it is 1.1 m from the bottom of the tank? (Round
your answer to three decimal places.)
2.At a given moment, a plane passes directly above a radar
station at an altitude of 6 km. The plane's speed is 900 km/h. How
fast is the distance between the plane...

A plane flying horizontally at an altitude of 2 mi and a speed
of 540 mi/h passes directly over a radar station. Find the rate at
which the distance from the plane to the station is increasing when
it is 4 mi away from the station. (Round your answer to the nearest
whole number.)
mi/h

A plane flying horizontally at an altitude of 1 mi and a speed
of 470 mi/h passes directly over a radar station. Find the rate at
which the distance from the plane to the station is increasing when
it is 2 mi away from the station. (Round your answer to the nearest
whole number.)
mi/h

4. An air plane flies horizontally with
X-velocity V0x= 360 m/s at
an altitude (height above the ground)=H=Dy= 3645
m. A bag of mass M=40 Kg falls off from
the plane, and moves to the ground in a parabolic path without air
resistance while the plane ciontinues to fly horizontally. Use
g=10 m/s2 and V0Y=0
Part A
The time the bag takes to hit the ground is t=____
seconds
The time the bag takes to hit the ground is t=____...

A plane flying horizontally at an altitude of 5 mi and a speed
of 470 mi/h passes directly
over a radar station. Find the rate at which the distance from
the plane to the station is increasing
when it is 7 mi away from the station. For full credit I expect
to see a well-labeled picture. Show all
work. Round your final answer to the nearest whole number. Do
not round intermediate values.
Include units of measure in your answer.

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