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September 18, 2019

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

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