#2 [Airliner Takeoff] A Delta Airlines CRJ-200 twin- engine jet airliner serving
ID: 1884430 • Letter: #
Question
#2 [Airliner Takeoff] A Delta Airlines CRJ-200 twin- engine jet airliner serving Ithaca's airport takes off starting from rest in a time of 28 s and a runway distance of 1200 m. (a) Estimate the airliner's acceleration during its takeoff run (in m/s2 and gs) and its speed as it lifts off the runway (in m/s and mi/h). Assume constant acceleration. Draw a velocity vs. time graph to illustrate your reasoning. Do your answers seem physically reasonable? Explain briefly (b) The airliner's acceleration actually decreases slightly but steadily as it picks up speed and air drag acts. Accounting for this, how would your answers be changed for the plane's calculated initial acceleration, its final acceleration just before liftoff, and its liftoff speed, based orn the information given above? Illustrate and answer this by drawing a 2nd velocity os. time graph on the same axes as your 1st. Remember that the total distance trawelled should be the same for both graphs (1200 m). Please be sure your reasoning is clear.Explanation / Answer
a] use S = ut + (1/2)at2
1200 = 0 + (1/2)a(28)2
a = 3.061 m/s2 = 0.312g
in this time, v = u + at = 85.714 m/s
this is the speed as the plane lifts off.
this speed corresponds to about 308 km/hr which is reasonable physically for achieving a lift.
The velocity vs time graph will be a straight line with slope being equal to dv/dt = a = 3.061 m/s2 and y intercept as c = 0.
b] The final acceleration will be lesser than the initial acceleration due to the air drag. This means that the v-t graph will no longer be a straight line but instead be a curve whose slope decreases with time. However, the distance traveled in both the cases must be the same which means that the area under the curve for both the cases will be equal. This implies that the liftoff speed will be smaller at t = 28s.
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