A jet aircraft with mass of 643,826 kilograms is flying straight upward.  At an instant the plane's engine is producing an upward thrust (force) of 5,615,378 Newtons and air resistance is exerting a force of 50,000 Newtons downward.  What is the acceleration of the plane in m/s2 at that instant?
Note: In this problem, we define "up" as positive.

To find the acceleration of the jet aircraft, we can apply **Newton's Second Law of Motion**, which states:

\[
F_{\text{net}} = m a
\]

Where:
- \(F_{\text{net}}\) is the net force acting on the aircraft,
- \(m\) is the mass of the aircraft,
- \(a\) is the acceleration of the aircraft.

### Step 1: Identify the forces involved
- **Thrust (upward)**: \(F_{\text{thrust}} = 5,615,378 \, \text{N}\) (positive since upward)
- **Air resistance (downward)**: \(F_{\text{air}} = 50,000 \, \text{N}\) (negative since downward)
- **Gravitational force (weight)**: \(F_{\text{gravity}} = m \cdot g = 643,826 \, \text{kg} \cdot 9.81 \, \text{m/s}^2 = 6,314,883.1 \, \text{N}\) (negative since downward)

### Step 2: Calculate the net force
\[
F_{\text{net}} = F_{\text{thrust}} - F_{\text{air}} - F_{\text{gravity}}
\]
\[
F_{\text{net}} = 5,615,378 \, \text{N} - 50,000 \, \text{N} - 6,314,883.1 \, \text{N}
\]
\[
F_{\text{net}} = -749,505.1 \, \text{N}
\]

This means the net force is **downward**.

### Step 3: Apply Newton’s Second Law
\[
F_{\text{net}} = m \cdot a
\]
\[
-749,505.1 \, \text{N} = 643,826 \, \text{kg} \cdot a
\]

Solve for \(a\):
\[
a = \frac{-749,505.1 \, \text{N}}{643,826 \, \text{kg}} \approx -1.164 \, \text{m/s}^2
\]

### Final Answer
The acceleration of the plane is approximately:

\[
a \approx -1.164 \, \text{m/s}^2
\]

This negative value indicates that the plane is **decelerating** (slowing down) at the given instant.

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Do you need any clarifications or further details?

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1. How would the acceleration change if the thrust increased?
2. What would the acceleration be if air resistance were doubled?
3. How does gravitational force affect acceleration in this scenario?
4. What does a positive or negative acceleration mean in terms of direction?
5. How would mass change affect the acceleration?

**Tip:** Be mindful of signs (+ or -) when working with forces and direction—especially in multi-force problems!

A jet aircraft with mass of 643,826 kilograms is flying straight upward. At an instant the plane's engine is producing an upward thrust (force) of 5,615,378 Newtons and air resistance is exerting a force of 50,000 Newtons downward. What is the acceleration of the plane in m/s2 at that instant? Note: In this problem, we define 'up' as positive.

Determine the acceleration of a jet aircraft with a mass of 643,826 kg flying upward with a thrust of 5,615,378 N against 50,000 N air resistance. Using Newton’s Second Law, learn how forces affect motion with detailed calculations suitable for high school and college physics.

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