To find the acceleration required for a jet to reach the liftoff speed from a starting velocity of 0 m/s, we can use the kinematic equation that relates acceleration, initial velocity, final velocity, and distance. The formula is:
\[ v^2 = u^2 + 2a s \]
Where:
- \( v \) is the final velocity (85 m/s, the liftoff speed)
- \( u \) is the initial velocity (0 m/s, since the jet starts from rest)
- \( a \) is the acceleration (what we need to find)
- \( s \) is the distance over which the acceleration occurs (the length of the aircraft carrier, 260 m)
Now we can substitute the known values into the equation:
\[ (85 , \text{m/s})^2 = (0 , \text{m/s})^2 + 2 a (260 , \text{m}) \]
Calculating \( (85 , \text{m/s})^2 \):
\[ 85^2 = 7225 , \text{m}^2/\text{s}^2 \]
Now substituting this into the equation:
\[ 7225 = 0 + 2 a (260) \]
This simplifies to:
\[ 7225 = 520 a \]
Now we can solve for \( a \):
\[ a = \frac{7225}{520} \]
Calculating the acceleration:
\[ a = 13.902 , \text{m/s}^2 \]
Therefore, the required acceleration for the jet to reach the liftoff speed of 85 m/s in 260 m is approximately 13.90 m/s².