A Cessna aircraft has a lift-off speed of 120 km/h.

(a)What minimum constant acceleration does this require if the aircraft is to be airborne after a take=off of 240m?

Work: 120 km/h-->33.3 m/s
(33.3 m/s)^2= (16.7 m/s)^2 + 2a(240 m)
a= 1.73 m/s^2
[What did I do wrong?]

(b)How long does it take the aircraft to be airborne?

Answer in back of book: (a) 2.32 m/s^2
(b) 14.4 s

I got the answer to Part A and B.

Part A. (33.3)^2-0(velocity initial) / 2(240) = a
1108.89/480 = 2.32 (rounded)

Part B. (240m)(33.3m/s) x 2 = 14.4

I got the right answer, but the calculation does not make sense.

(240m)/(33.3 m/s) x 2 = 14.4s

why would you multiply by 2?

Part 2.

time= distance/average velocity

or

vf= vi+ at at takeoff, solve for t.
33.3=0+2.32 t

Where did you get the 33.3 m/s in 120 km/h?

What are the steps and equation used to solve this problem?

In order to find out what you did wrong in part (a) of the problem, let's go through the calculation again step by step.

First, let's convert the lift-off speed from kilometers per hour (km/h) to meters per second (m/s).

Given: Lift-off speed = 120 km/h

To convert km/h to m/s, we need to multiply by a conversion factor of 1000/3600:

120 km/h * (1000 m / 3600 s) ≈ 33.33 m/s

So you are correct in converting the lift-off speed to approximately 33.33 m/s.

Next, let's set up the equation of motion to find the minimum constant acceleration required for the aircraft to be airborne after a take-off distance of 240 m.

Using the kinematic equation:

v^2 = u^2 + 2as

where:
v = final velocity (which is 0 m/s since the aircraft is airborne)
u = initial velocity (33.33 m/s)
a = acceleration (unknown)
s = displacement (240 m)

Plugging in the values:

0^2 = (33.33 m/s)^2 + 2a(240 m)

Simplifying:

0 = 1111.09 m^2/s^2 + 480a m

Now, rearrange the equation to solve for acceleration:

480a = -1111.09 m^2/s^2

a = -1111.09 m^2/s^2 / 480

a ≈ -2.32 m/s^2

It seems that you made a sign error in your calculation. The negative sign indicates that the acceleration acts in the opposite direction of the initial velocity.

So, the correct minimum constant acceleration required for the aircraft to be airborne is approximately -2.32 m/s^2.

Moving on to part (b) of the problem, we need to find the time it takes for the aircraft to be airborne.

Using the equation of motion:

v = u + at

where:
v = final velocity (0 m/s)
u = initial velocity (33.33 m/s)
a = acceleration (-2.32 m/s^2)
t = time (unknown)

Plugging in the values:

0 = 33.33 m/s + (-2.32 m/s^2) * t

Simplifying:

2.32t = 33.33

t ≈ 33.33 / 2.32

t ≈ 14.39 s

So, the correct answer for part (b) is approximately 14.4 s.

In summary, the correct answers are:
(a) The minimum constant acceleration required is approximately -2.32 m/s^2.
(b) The time it takes for the aircraft to be airborne is approximately 14.4 s.

Why do you think it had a starting velocity? Most airplanes start at the end of the runway with zero velocity.

how would I find part(b)?