Chapter 2, Problem 23P

To determine

The length of the runway needed by the light plane

Answer to Problem 23P

181.5 m

Explanation of Solution

Given:

Initial velocity of the plane $=v_i=0\frac{\text{m}}{\text{s}}$

Final velocity of the plane $=v_f=33\frac{\text{m}}{\text{s}}$

Acceleration of the plane $=a=3\frac{\text{m}}{{\text{s}}^{\text{2}}}$

Length of the runway $=L$

Displacement of the plane $=\Delta x=L$

Formula Used:

Acceleration is given as

  $a=\frac{v^2{}_f-v^2{}_i}{2\Delta x}$

Calculation:

Consider the motion of the plane while speeding up:

Acceleration of the plane is given as

  $a=\frac{v^2{}_f-v^2{}_i}{2\Delta x}$

Inserting the values

  $\begin{array}{l}3=\frac{{33}^2-0^2}{2L}\\ L=\frac{{33}^2-0^2}{2(3)}\\ L=181.5\text{m}\end{array}$

Conclusion:

Therefore, length of runway is 181.5 m.