# Math Help - Fibonacci Higher Order Question

1. ## Fibonacci Higher Order Question

1. When a Navy fighter lands on an aircraft carrier, a steel cable is used to slow the jet to a stop before it falls off the ship. The fighter stops after a displacement of 100m [w] and a time of 4.0s.

a) Determine the initial velocity of the fighter including direction.

I was thinking of using the equation d = V1(t) + 1/2a(t)^2. The only problem is, no acceleration is given. Would I just leave the acceleration at 0? Or do I have to calculate it using the equation v = a(t). Perhaps I could find delta velocity by dividing 100m [w] by 4.0s? Then divide 25m/s[w] by 4s to get the acceleration? This question has no answers to check, so I just want to be sure I've got the right idea.

1. When a Navy fighter lands on an aircraft carrier, a steel cable is used to slow the jet to a stop before it falls off the ship. The fighter stops after a displacement of 100m [w] and a time of 4.0s.

a) Determine the initial velocity of the fighter including direction.

I was thinking of using the equation d = V1(t) + 1/2a(t)^2. The only problem is, no acceleration is given. Would I just leave the acceleration at 0? Or do I have to calculate it using the equation v = a(t). Perhaps I could find delta velocity by dividing 100m [w] by 4.0s? Then divide 25m/s[w] by 4s to get the acceleration? This question has no answers to check, so I just want to be sure I've got the right idea.
1. Consider stopping the aircraft as an uniform accelerated movement. Then

$d = \frac12 \cdot a \cdot t^2$

2. With the given values (d = 100 m, t = 4 s) you'll get $a = 12.5\ \frac{m}{s^2}$

3. When the aircraft has stopped it's speed is zero:

$v(4) = 0 = v(0)-a \cdot t$

Calculate v(0).

I'm curious: Why did you use this headline?

I used this headline because that is what the sheet is titled. My teacher said that all Fibonacci questions that we get (this is the first) will appear on the final exam at the end of the semester. This question is supposed to be the hardest one we've received yet next to the bonus question he gave.

Ever since we've started the kinematic equations chapter, he gave us 8 equations to use:

2. DeltaVelocity = (AccelerationAverage)(DeltaTime)

3. VelocityAverage = (VelocityInitial + VelocityFinal) / 2

4. VelocityFinal = VelocityInitial + (Acceleration)(DeltaTime)

5. DeltaDisplacement = ((VelocityInitial + VelocityFinal) / 2)(DeltaTime)

6. DeltaDisplacement = (VelocityInitial)(DeltaTime) + 1/2(Acceleration)(DeltaTime)^2

7. DeltaDisplacement = (VelocityFinal)(DeltaTime) - 1/2(Acceleration)(DeltaTime)^2

8. VelocityFinal = VelocityInitial + 2(Acceleration)(DeltaDisplacement)

We always solve equations using the GRASP method. Though, I wasn't sure if the equation d = 1/2(a)(t)^2 was a manipulation of Equation 6. Is it even possible to solve this problem using (and rearranging the variables of) the 8 given equations? Or will some questions require different equations, like this one?

Anyways, I applied the values to that equation, and got 12.5m/s^2 like you said. The next equation that you gave I haven't seen before. It looked like equation 6 (is it?), so I applied d = 100m [W], t = 4s, a = 12.5m/s^2 to the equation. I got my initial velocity at 0 m/s.

Question 1. b) is asking me to plot a velocity time graph for the fighter. I'm guessing there will simply be a horizontal line on the x-axis at 0 velocity? Or was the equation you gave different than 6 and the initial velocity was more than 0? I'm kinda confused right now.

Question c) asks, "Determine the acceleration of the fighter including direction (do not use your result from part (a) in this calculation)."

Hasn't the acceleration already been solved?

And finally, question d asks to sketch a displacement time graph for the fighter.

I'm guessing that for this question, I could find the displacement from the velocity time graph using 1/2bh (area)?

4. I solved the second equation you gave me and I got this:

v(4) = 0 = (v)(0) - AT
0 - AT = v(0) <--v1 / Initial Velocity Symbol?
0 - (12.5m/s^2)(4s) = v(0)
0 - 50m/s = v(0)
-50m/s [W]= v(0)
50m/s [E] = V(0)

The initial velocity is in the opposite direction?

5. When the question asks for the initial velocity, is that including the velocity the plane has in the air, or just when it reaches the 100m distance? This is the diagram provided with the question.