Final answer:
The emergency kit will take approximately 6.92 seconds to fall from a height of 132 meters with a constant vertical acceleration of -6.89 m/s², assuming no air resistance and wind.
Step-by-step explanation:
The student has posed a question about the time it takes for an emergency kit to fall from a rescue plane flying horizontally. Using the given vertical acceleration of -6.89 m/s² and the initial height of 132 m, we can calculate the duration of the fall. Since air resistance and wind are negligible, we can apply the kinematic equations for uniformly accelerated motion.
To calculate the falling time t, we use the equation:
h = v0t + ½at²
Where h is the height the kit falls (132 m), v0 is the initial velocity (0 m/s, since it is dropped and only has horizontal velocity), a is the constant vertical acceleration (-6.89 m/s²), and t is the time in seconds.
By rearranging the equation to solve for time and substituting the known values, we get:
0 = 132 + ½(-6.89)t²
Thus, after solving for t, we find that it will take approximately 6.92 seconds for the emergency kit to reach the ground.