Question

An engineer is to design a runway to accommodate airplanes that must gain a ground speed of 360 km/h (approx. 225 mi/h) before they can take off. These planes are capable of being accelerated uniformly at the rate of 3.60x104 km/h2How many kilometers long must the runway be?How many seconds will a plane need to accelerate to take-off speed?please help me solve this

Answer 1

Given:

Final Velocity = 360 km/h

Acceleration, a = 3.60 x 10⁴ km/h²

Let's solve for the following:

• (a). How many kilometers long must the runway be?

To find the length of the runway, apply the formula:

`v^2_f=v^2_i+2ad`

Where:

vf is the final velocity = 360 km/h

vi is the initail velocity = 0 km/h

a is the acceleration = 3.60 x 10⁴ km/h²

d is the distance the plane will cover which in this case is the length of the runway.

Rewrite the equation for d:

`d=(v^2_f-v^2_i)/(2a)`

Input values in the equation:

`\begin{gathered} d=(360^2-0^2)/(2(3.60*10^4)) \\ \\ d=(360^2)/(2(3.60*10^4)) \\ \\ d=(129600)/(72000) \\ \\ d=1.8\text{ km} \end{gathered}`

Therefore, the runway must be 1.8 kilometers long.

• (b). How many seconds will a plane need to accelerate to take-off speed?

To find the number of seconds it will take, apply the formula:

`v_f=v_i+at`

Where t is the time.

Rewrite the equation for t:

`t=(v_f-v_i)/(a)_{}`

Thus, we have:

`\begin{gathered} t=(360-0)/(3.60*10^4) \\ \\ t=(360)/(3.60*10^4) \\ \\ t=0.01 \end{gathered}`

The time is 0.01 hour.

To convert to seconds, we have:

Where:

1 hour = 3600 seconds

0.01 hour = 3600 x 0.01 = 36 seconds

Therefore, the plane will need to accelerate for 36 seconds before take off.

ANSWER:

(a) 1.8 km

(b) 36 seconds