A plane making an emergency landing first touches the ground while going 120 MPH
ID: 1528889 • Letter: A
Question
A plane making an emergency landing first touches the ground while going 120 MPH. After the plane skids on the ground for 2.7 seconds, its velocity is reduced to 60 MPH. During this 2.7 sec interval, what is the average acceleration of the plane while skidding on the ground and how far did the plane travel while skidding for this 2.7 seconds?
Convert your velocities to meters/second so the displacement and acceleration are in meters and m/s2.
The following questions can be filled in any order. REMEMBER TO SAVE ANSWERS OFTEN.
Put the origin of your coordinate system at the point where the plane first touches the ground and the positive x-axis in the direction of the planes' motion.
1-SORT
Initial Position, Xo at the start of the skid (m)
2- SORT
Convert the initial velocity from Miles per Hour (MPH) to meters / sec
Initial Velocity, Vox at start of skid in METERS per SECOND (m/s)
3-SORT
The acceleration, ax and final position, xf are unknown and you will solve for them.
Convert the final velocity at the end of the time interval from Miles per Hour (MPH) to m/s
Finial Velocity, Vfx at end of time interval in METERS Per SECOND (m/s)
4-SORT
Elapsed time, t, during skidding (seconds)
5- GUESSTIMATE
The plane is slowing down and traveling to the right. What statement is true for the acceleration?
The acceleration will be less than zero (vector points to the left) (includes direction sign)
The acceleration will equal zero
The acceleration will be greater than zero (vector points to the right) (includes direction sign)
6- SOLVE
Final Position, Xf (equals the Displacement during the time interval) (m) (Will be positive)
(This is how far the plane travels after it first touches the ground)
7-SOLVE
Avg. Acceleration, ax, during the time interval (m/s2) (can be negative or positive)
8-CHECK
You could have bounded the distance the plane travels (Xf) by estimating the time as 3 seconds. Then, you could assume two cases:
Case 1. The plane travels at the rounded initial velocity and does not slow down. This gives you an upper bound on Xf 3(50) 150m
Case 2: The plane travels at the rounded final velocity for the entire skid. This gives you a lower bound on Xf (3)(25) 75m
Did your final position, Xf , land between these bounds?
The acceleration will be less than zero (vector points to the left) (includes direction sign)
The acceleration will equal zero
The acceleration will be greater than zero (vector points to the right) (includes direction sign)
6- SOLVE
Final Position, Xf (equals the Displacement during the time interval) (m) (Will be positive)
(This is how far the plane travels after it first touches the ground)
7-SOLVE
Avg. Acceleration, ax, during the time interval (m/s2) (can be negative or positive)
8-CHECK
You could have bounded the distance the plane travels (Xf) by estimating the time as 3 seconds. Then, you could assume two cases:
Case 1. The plane travels at the rounded initial velocity and does not slow down. This gives you an upper bound on Xf 3(50) 150m
Case 2: The plane travels at the rounded final velocity for the entire skid. This gives you a lower bound on Xf (3)(25) 75m
Did your final position, Xf , land between these bounds?
A plane making an emergency landing first touches the ground while going 120 MPH. After the plane skids on the ground for 2.7 seconds, its velocity is reduced to 60 MPH. During this 2.7 sec interval, what is the average acceleration of the plane while skidding on the ground and how far did the plane travel while skidding for this 2.7 seconds? Convert your velocities to meters/second so the displacement and acceleration are in meters and m/s^2. The following questions can be filled in any order. REMEMBER TO SAVE ANSWERS OFTEN. Put the origin of your coordinate system at the point where the plane first touches the ground and the positive x-axis in the direction of the planes' motion. 1-SORT Initial Position, Xo at the start of the skid (m) 2- SORT Convert the initial velocity from Miles per Hour (MPH) to meters/sec Initial Velocity, V_ox at start of skid in METERS per SECOND (m/s) 3-SORT The acceleration, a_x and final position, x_f are unknown and you will solve for them. Convert the final velocity at the end of the time interval from Miles per Hour (MPH) to m/s Finial Velocity, V_fx at end of time interval in METERS Per SECOND (m/s) 4-SORT Elapsed time, t, during skidding (seconds) 5- GUESSTIMATE The plane is slowing down and traveling to the right. What statement is true for the acceleration? The acceleration will be less than zero (vector points to the left) (includes direction sign) The acceleration will equal zero The acceleration will be greater than zero (vector points to the right) (includes direction sign) 6- SOLVE Final Position, X_f (equals the Displacement during the time interval) (m) (Will be positive) (This is how far the plane travels after it first touches the ground) 7-SOLVE Avg. Acceleration, a_x, during the time interval (m/s^2) (can be negative or positive) 8-CHECK You could have bounded the distance the plane travels (X_f) by estimating the time as 3 seconds. Then, you could assume two cases: Case 1. The plane travels at the rounded initial velocity and does not slow down. This gives you an upper bound on X_f 3(50) 150m Case 2: The plane travels at the rounded final velocity for the entire skid. This gives you a lower bound on X_f (3)(25) 75m Did your final position, X_f, land between these bounds?Explanation / Answer
A plane making an emergency landing first touches the ground while going 120 MPH. After the plane skids on the ground for 2.7 seconds, its velocity is reduced to 60 MPH. During this 2.7 sec interval, what is the average acceleration of the plane while skidding on the ground and how far did the plane travel while skidding for this 2.7 seconds?
Initial velocity of plane, = 120 MPH = 53.64 m/s
t = 2.7 s
Final velocity of plane, = 60 MPH = 26.8 m/s
vf = vi + a*t
26.8 = 53.64 + a * 2.7
a = - 9.94 m/s^2
Average acceleration of the plane, a = - 9.94 m/s^2
-ve sign shows plane is de-accelerating !!!
Distance travelled,
vf^2 = vi^2 + 2*a*s
26.8^2 = 53.64^2 - 2*9.94*s
s = 108.6 m
Distance travelled while skidding, s = 108.6 m
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