Final answer:
To find the distance the airplane travels across the runway before taking off, we apply the kinematic equation d = ut + (1/2)at^2, and calculate that the airplane travels 121.5 meters.
Step-by-step explanation:
The student is asking about the distance an airplane travels across the runway before it takes off, given a uniform acceleration and a time period. To solve for the distance, we can use the kinematic equation for uniformly accelerated motion:
\( d = ut + \frac{1}{2}at^2 \)
where \( d \) is the distance, \( u \) is the initial velocity (which is 0 m/s since it starts from rest), \( a \) is the acceleration, and \( t \) is the time period.
Substituting the given values:
\( d = 0 \times 9 + \frac{1}{2}(3\, m/s^2)(9\, s)^2 \)
\( d = \frac{1}{2}(3)(81) \)
\( d = \frac{243}{2} \)
\( d = 121.5\, m \)
Therefore, the airplane travels a distance of 121.5 meters across the runway before taking off, which corresponds to answer choice C)