Question
In order for a modern air superiority fighter plane to become airborne, they must reach a speed of approximately 85 meters per second. If the average jet engine can provide an acceleration of 11.05 m/s, how long will it take for a fighter jet to reach takeoff speed from a starting velocity of 0 m/s? Show all work
Answers
GPT-4o mini
To find the time it takes for a fighter jet to reach takeoff speed from a starting velocity of 0 m/s, we can use the equation of motion that relates acceleration, final velocity, initial velocity, and time. The equation is:
\[
v = u + at
\]
Where:
- \( v \) is the final velocity (takeoff speed),
- \( u \) is the initial velocity,
- \( a \) is the acceleration,
- \( t \) is the time.
Given:
- Final velocity \( v = 85 \, \text{m/s} \)
- Initial velocity \( u = 0 \, \text{m/s} \)
- Acceleration \( a = 11.05 \, \text{m/s}^2 \)
We can substitute these values into the equation:
\[
85 \, \text{m/s} = 0 \, \text{m/s} + (11.05 \, \text{m/s}^2) \cdot t
\]
This simplifies to:
\[
85 = 11.05t
\]
Next, we will solve for \( t \):
\[
t = \frac{85}{11.05}
\]
Calculating the right side:
\[
t \approx 7.69 \, \text{s}
\]
Thus, it will take approximately **7.69 seconds** for the fighter jet to reach takeoff speed of 85 m/s from a starting velocity of 0 m/s with an acceleration of 11.05 m/s².
\[
v = u + at
\]
Where:
- \( v \) is the final velocity (takeoff speed),
- \( u \) is the initial velocity,
- \( a \) is the acceleration,
- \( t \) is the time.
Given:
- Final velocity \( v = 85 \, \text{m/s} \)
- Initial velocity \( u = 0 \, \text{m/s} \)
- Acceleration \( a = 11.05 \, \text{m/s}^2 \)
We can substitute these values into the equation:
\[
85 \, \text{m/s} = 0 \, \text{m/s} + (11.05 \, \text{m/s}^2) \cdot t
\]
This simplifies to:
\[
85 = 11.05t
\]
Next, we will solve for \( t \):
\[
t = \frac{85}{11.05}
\]
Calculating the right side:
\[
t \approx 7.69 \, \text{s}
\]
Thus, it will take approximately **7.69 seconds** for the fighter jet to reach takeoff speed of 85 m/s from a starting velocity of 0 m/s with an acceleration of 11.05 m/s².