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Aircraft
Trajectory
Answers
UNIT ANALYSIS:
In the table provided, give the correct units in both the English and
the Metric systems.
QUANTITY
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ENGLISH
UNIT
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METRIC
UNIT
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time
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seconds
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seconds
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distance
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feet
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meters
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mass
|
slug
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kilogram
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force
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pounds
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Newtons
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velocity
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feet/second
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meters/second
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acceleration
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feet/second
squared
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meters/second
squared
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PROBLEMS:
Solve the following problems and show your work in the space provided. (Don't
forget to label your answer with the proper units.)
- An airplane begins
its takeoff run at a speed of 40 knots. If the runway is 6,000 ft long
and it takes 20 seconds to reach liftoff speed, what acceleration must
the pilot maintain for takeoff? (One Knot=1.69 ft/sec)
6,000 ft = a(20 sec)2/2 + [(40 kts x
1.69 ft/sec/kts)(20 sec)] a = 23 ft/sec
- An 8,200 kg airplane
touched its runway at 65 m/s and came to a stop in 25 seconds.
Find
(A) negative acceleration
0 = a(25 sec) + 65 m/s a = -2.6 m/ sq s
(B) the length
of the runway
X - X0 = (-2.6 m/sq s)(25 sec)/2
+ 65 m/s (25 sec) = 1592.5 m
- A 9,600 lb airplane
takes off at 160 ft/sec. If it accelerates at a constant rate of 30
ft/sec2:
- How
much time is needed to reach takeoff speed?
160 m/s = (30 ft/sq sec)t + 0m/s t=5.3
sec
- What length
airstrip is used?
X - X0 = (30 ft/sq sec)(5.3
sec) = 80 ft
- What force
is needed to produce this acceleration?
F = (9600 lbs/32.2 ft/sl)(30 ft/ sq
sec) = 8944 lbs
- A military airplane
flying at a speed of 350 m/s must make a supply drop. The pilot releases
the supply crate 2,400 m before the drop target. How long will it take
for the crate to hit the ground?
0 = (9.8 m/sq s)t/2 + (350 m/s) + 2,400
m
t = 6.22 sec (by the quadratic equation)
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