Question

A jet needs to reach a "lift-off' speed of 120 m/s before it can leave the ground. How quickly must
the jet accelerate if the run way has a length of 322 m?

Answer 1

The jet must accelerate in 5.37 s if it must reach the lift-off speed

From the question given above, the following data were:

Initial velocity (u) = 0 m/s

Final velocity (v) = 120 m/s

Distance (s) = 322 m

Time (t) =?

The time needed for the jet to accerate can be obtained as follow:

$s = \frac{(v + u)t}{2} \\ \\ 322 = \frac{(120 + 0)t}{2} \\ \\ 322 = \frac{120t}{2} \\ \\ cross \: multiply \\ \\ 120t = 322 \times 2 \\ \\ 120t = 644 \\ \\ divide \: both \: side \: by \: 120 \\ \\ t = \frac{644}{120}$

t = 5.37

Thus, the jet must accelerate in 5.37 s in order to reach the lift-off speed

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Answer 2

As the jet leaves the ground, it accelerates at a rate of 22.4 ms-2.

We have the following information from the question;

Final velocity = 120 m/s

Initial velocity = 0 m/s

Distance covered = 322 m

Acceleration = ?

Using the equation;

v^2 = u^2 + 2as

v = final velocity

u = initial velocity

a = acceleration

s = distance

(120)^2 = 0^2 + (2 × a × 322)

14400 = 644a

a = 14400/644

a = 22.4 ms-2

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