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Chapter 1: Q108P (page 1)

Question: A jumbo jet must reach a speed of 360 km/hron the runway for takeoff. What is the lowest constant acceleration needed for takeoff from a 1.80 km runway?

Short Answer

Expert verified

The lowest constant acceleration of the jumbo jet is 2.78 m/s2.

Step by step solution

01

Given data

Initial speed, v0=0km/h

Final speed, role="math" localid="1650541085444" v=360km/h

Distance,x=1.80km

02

Understanding the kinematic equations Kinematic equations describe the motion of an object with constant acceleration. These equations can be used to determine the acceleration.

The expression for the kinematic equations of motion are given as follows:

v2=v02+2ax 鈥� (i)

Here, v0is the initial velocity, vis the final velocity, ais the acceleration and xis the displacement.

03

Determination of the lowest constant acceleration.

Convert the velocity from km/h to m/s as:

v=360kmh脳1000m1km脳1h3600s=100m/s

Using equation (i), the acceleration is calculated as follows:

role="math" localid="1650541810726" a=v2-v022x=100m/s2-0m/s22脳1.8办尘脳1000m1km=2.78m/s2

Thus, the lowest constant acceleration needed for the jumbo jet is 2.78m/s2.

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