An airplane started its flight from point A towards point B at the same time as a helicopter started its flight from point B towards point A. When they meet, a helicopter flew 100 miles less than an airplane. After the meeting point, a helicopter needs 3 hours to reach point A, and an airplane needs 1 hour and 20 minutes to reach point B. Find the average speed of a helicopter and the distance between points A and B.
Answers
Answer:
getting from a departure point to a destination in
the least possible time without losing your way. If
you are a pilot of a rescue helicopter, you need to
know the following:
Start point (point of departure)
End point (final destination)
Direction of travel
Distance to travel
Characteristics of type of aircraft being flown
Aircraft cruising speed
Aircraft fuel capacity
Aircraft weight and balance information
Capability of on-board navigation equipment
Some of this information can be obtained from the
aircraft operation handbook. Also, if taken into
consideration at the start of the aircraft design
they help an aeronautical engineer to develop a
better aircraft.
VECTORS: A REMINDER
A vector quantity has both magnitude and
direction. It can be represented geometrically
using a line segment with an arrow. The length of
the vector represents the magnitude drawn to
scale and the arrow indicates the direction.
Velocity is an example of a vector quantity.
AIR SPEED / GROUND SPEED / WIND SPEED
An aircraft's speed can be greatly enhanced or
diminished by the wind. This is the reason for the
consideration of two speeds: ground speed and
air speed. Ground speed is the speed at which
an aircraft is moving with respect to the ground.
Air speed is the speed of an aircraft in relation to
the surrounding air. Wind speed is the physical
speed of the air relative to the ground. Air speed,
ground speed and wind speed are all vector
quantities. The relationship between the ground
speed Vg
, wind speed Vw
and air speed Va
is
given by
w . Vg Va V
= +
SCENARIO
Knowledge of aircraft navigation is vital for safety.
One important application is the search and
rescue operation. Imagine that some people are
stuck on a mountain in bad weather. Fortunately,
with a mobile phone, they managed to contact the
nearest Mountain Rescue base for help. The
Mountain Rescue team needs to send a
helicopter to save these people. With the signal
received from the people on the mountain, they
determine that the bearing from the helipad (point
A) to the mountain (point C) is 054° (i.e. approx.
north-east). Also the approximate distance is
calculated to be 50 km.
Figure-1
Assume that the rescue helicopter can travel at a
speed of 100 knots and a 20-knot wind is blowing
on a bearing of 180°. The knot is the standard unit
for measuring the speed of an aircraft and it is
equal to one nautical mile per hour.
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It is defined as follows in SI:
1 international knot = 1 nautical mile per hour
= 1.852 km/hr exactly
= 1.151 miles/hr approx.
= 0.514 m/sec approx.
GROUND SPEED AND COURSE
We can quickly and accurately determine the
ground speed and course using a sketch to
visualise the problem as shown in Figure-1
above. Anticipating the effect of wind, the
helicopter needs to fly on a heading aiming at a
point B that is slightly more northerly