47.1k views
1 vote
A rescue plane is flying horizontally at a height of 132 m above the ground. The pilot spots a survivor and releases an emergency kit with a parachute. The kit descends at a constant vertical acceleration of -6.89 m/s, and the initial plane horizontal speed is 68.9 m/s. Assuming air resistance and wind are negligible, how long will the emergency kit be falling through the air?

User Foad
by
7.2k points

1 Answer

3 votes

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.

User StephenD
by
7.5k points