# Exercise 1: rectilinear motion | Mathematics homework help

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Exercise 1: Rectilinear Motion

Uniformly Accelerated Rectilinear Motion and Newton’s Law of Momentum
Equations to use (remember to keep track of units):

F = ma                                     m = W/g
T-D-f = ma                              VF 2 = VI 2 + 2 a s
VF = VI 2 + a t                                   Takeoff distance (s) = VF 2 /2a
KE = ½ m                               V2 PE = Wh
HP= T*Vkts /325                    sin(γ) = (ROCkts)/(Vkts)
1 kt = 1.69 ft/sec                     g = 32.2 ft/sec2

Givens: (Questions 1 to 8)

Gross Weight                          = 100,000 pounds
Average Drag                          = 5,000 pounds
Average Friction Force           = 1,000 pounds
Average Thrust                       = 34,000 pounds
Lift Off Speed                        = 150 Knots True Airspeed

1. Compute the acceleration on the aircraft during the takeoff roll (ft / sec 2).

2. What would be the length of the takeoff run (ft)?

3. How long would it take until liftoff once the takeoff roll is started (sec)?

4. Given the information shown above, determine how fast this airplane should be going when it passes the 2000-foot runway marker (2000 feet from the start of the takeoff roll)? Please express your answer in knots.

5. What is the power (HP) of the aircraft engines after takeoff at Average Thrust at 250KTAS?

6. What is the Kinetic Energy (ft-lb) of the aircraft after climbing out at 250 KTAS with the new weight at 95,000 lb?

7. What is the Potential Energy (ft-lb) of the aircraft after climbing out to 10,000 ft above sea level with the new weight at 95,000 lb?

8. What is the Angle of Climb (deg) for airplane at 250 KTAS with a climb rate of 4,000 ft/min?

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