Math Problem Statement

A 38000kg business jet takes off with the thrust for each of its two engines is 40000 N. Find the acceleration

Solution

To find the acceleration of the business jet, we can apply Newton's Second Law of Motion:

Fnet=maF_{\text{net}} = m \cdot a

Where:

  • FnetF_{\text{net}} is the total net force acting on the jet,
  • mm is the mass of the jet,
  • aa is the acceleration.

Step 1: Calculate the net force

The total thrust provided by both engines is:

Fnet=2×40,000N=80,000NF_{\text{net}} = 2 \times 40,000 \, \text{N} = 80,000 \, \text{N}

Step 2: Use Newton's Second Law to find the acceleration

Now, using Fnet=maF_{\text{net}} = m \cdot a, we can solve for the acceleration aa:

a=Fnetma = \frac{F_{\text{net}}}{m}

Substituting the given values:

a=80,000N38,000kg=2.11m/s2a = \frac{80,000 \, \text{N}}{38,000 \, \text{kg}} = 2.11 \, \text{m/s}^2

Thus, the acceleration of the jet is 2.11 m/s².

Would you like more details or have any questions?

Here are 5 related questions to expand the topic:

  1. What would happen to the acceleration if one engine fails?
  2. How would the acceleration change if the mass of the jet increased?
  3. How does air resistance affect the net force and acceleration in real-world conditions?
  4. What is the relationship between thrust, drag, and the final velocity of an aircraft?
  5. How would the jet's acceleration compare to that of a lighter plane with the same thrust?

Tip: Always ensure the forces are balanced or unbalanced when using Newton’s laws—this will determine if the object is accelerating.

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Math Problem Analysis

Mathematical Concepts

Newton's Second Law of Motion
Force
Mass
Acceleration

Formulas

F_net = m * a
a = F_net / m

Theorems

Newton's Second Law of Motion

Suitable Grade Level

Grades 9-11