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## Homework Statement

An airplane is approaching land with a speed 57 m/s and an angle 15° below the horizontal. The runway is 0.8 km long and the pilot can use the flaps and reverse the engine thrust, to provide a constant deceleration, only after she touches down at the beginning of the runway. How long will it take her to reach the end of the runway and come to a full stop?

## Homework Equations

## The Attempt at a Solution

My initial veocity is 57cos(15) which leaves me with a landing speed of 55.06m/s since the y-axis velocity cancels..I hope.

I have this solved, but trying two different methods (which should work) in order to verify the answer reveals two completely different answers.

Solving for acceleration:

[tex]v_f^2 = v_i^2 +2as \rightarrow (v_f^2 - v_i^2)/2s = a[/tex]

Plugging in the numbers I get a = -1.895 m/s^2

Here is where I run into a problem solving for t.

Method One:

[tex]v_f = v_i +at \rightarrow (v_f - v_i)/a = t[/tex]

Plugging in all of values I have t=29.055s

Method Two:

[tex]s_f = s_i + v_it + 1/2at^2[/tex]

Here I end up with a quadratic equation with these values:

A= -0.945

B= 55.06

C= 800

This gives me one useable number of 70s.(the other is -12)

If I use -800 for c I come up wtih two close values: 27.67 and 30.59. Now that I am thinking about it. I should use -800 here. But it still doesn't work.

Why is it I can't seem to use the position equation on this one?

Am I missing something that is giving me these two different values? I'd assume both should give me the same value since I am solving for t in both.

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