
Aircraft
Trajectory
Answers
UNIT ANALYSIS:
In the table provided, give the correct units in both the English and
the Metric systems.
QUANTITY

ENGLISH
UNIT

METRIC
UNIT

time

seconds

seconds

distance

feet

meters

mass

slug

kilogram

force

pounds

Newtons

velocity

feet/second

meters/second

acceleration

feet/second
squared

meters/second
squared

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  X_{0} = (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/sec^{2}:
 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  X_{0 }= (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)
