Question

Related Rates question: An airplane flying horizontally at a height
of 8000m with a speed of 100m/s passes directly over a pond. How
fast is its straight line distance from the pond increasing 1 min
later?

Answer #1

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.)

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

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

You drop a package from an airplane flying at a constant speed
in a straight horizontal line. From the same height and time, one
red ball is dropped and another blue ball is fired horizontally.
The air resistance can be neglected. Which will hit the ground
first, the package, the red ball, or the blue ball?
Include an explanation!

An airplane flying horizontally at an elevation of 0.75 km,
with a constant speed of 350 km/hr, over level ground, releases a
bundle of food supplies. What is its horizontal and vertical
velocity component just before hitting the ground? If the
airplane’s speed were instead, 450 km/hr, would the time of fall be
larger, smaller, or the same?

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.

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

QUESTION 3 An airplane flying at a speed of 600 km / h
to the north is held by a wind blowing at a speed of 50 km / h from
the north-east direction. What should be the speed and direction of
the plane to go in the same direction (north)?

An airplane is flying at a speed of 3.23 × 10^2 m/s in level
flight at an altitude of 9.05 × 10^2 m. A package is to be dropped
from the airplane to land on a target on the ground. Ignore air
resistance. At what horizontal distance away from the target should
the package be released so that it lands on the target? Express
your answer in meters.

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