Chapter 4, Problem 73A

To determine

The length of the runway for takeoff of the jet plane.

Answer to Problem 73A

The length of the runway for takeoff with speed $285\text{km}/\text{h}$ is $138.49\text{m}$ .

Explanation of Solution

Given Info:

The weight of the jet plane is, $W=2.75\times {10}^6\text{N}$ .

The forward force of the engine is, $F=6.35\times {10}^6\text{N}$ .

The speed of the jet plane is, $v=285\text{km}/\text{h}=79.17\text{m}/\text{s}$ .

Formula Used:

The expression to calculate the length of the runway is,

  $l=\frac{W{v}^2}{2gF}$

Calculation:

Substitute all the values in the above expression.

  $\begin{array}{c}l=\frac{\left(2.75\times {10}^6\text{N}\right){\left(79.17\text{m}/\text{s}\right)}^2}{2\left(9.8\text{m}/{\text{s}}^2\right)\left(6.35\times {10}^6\text{N}\right)}\\ =138.49\text{m}\end{array}$

Thus, the length of the runway for takeoff with speed $285\text{km}/\text{h}$ is $138.49\text{m}$ .