Solution to problems – class 9 – Set 1 Q 23

Problem Statement

An engineer is designing the runway for an airport.

Of the planes that will use the airport, the lowest acceleration rate is likely to be 3 m/s².

The takeoff speed for this plane will be 65 m/s.
Assuming this minimum acceleration, what is the minimum allowed length for the runway?

Solution

U = 0
V = 65 m/s
a = 3 m/s²

To find out the distance, we will use the following equation:
S = Ut + ½ a t²
as U = 0, the equation becomes    S = ½ a t² = ½ . 3. t² ……(1)

We will use the following eqn to find out the time required to attain this velocity.
 V = u + at
As U = 0, the eqn becomes V = at
t = V/a = 65/3 sec……(2)

Putting the value of time t in equation 1 we get S = ½ . 3. (65/3)²
= 704 m
So the minimum allowed length of the airport is 704 m