High School

An emergency relief plane is dropping a care package to a group of medical personnel working for a relief agency in an African village. The package is designed to land in a small lake, inflate an attached raft upon impact, and finally resurface with the raft side up.

The plane will be moving horizontally with a ground speed of 59.1 m/s. The package will be dropped a horizontal distance of 521 m from the intended target location.

At what altitude above the pond must the plane be flying in order to successfully accomplish this feat?

Answer :

Answer:

The altitude of the plane is 379.5 m.

Explanation:

Initial horizontal velocity, u = 59.1 m/s

Horizontal distance, d = 521 m

let the time taken by the packet to cover the distance is t.

Horizontal distance = horizontal velocity x time

521 = 59.1 x t

t = 8.8 s

let the vertical height is h .

Use second equation of motion in vertical direction.

[tex]h = u t + 0.5 gt^2\\\\h = 0 + 4.9 \times 8.8\times8.8\\\\h= 379.5 m[/tex]

Final answer:

The plane must be flying at an altitude of approximately 194.89 m above the pond.

Explanation:

To successfully drop the care package in the small lake, the plane must be flying at a certain altitude above the pond. We can use the horizontal distance and the ground speed of the plane to calculate the time it takes for the package to reach the target location. Then, using the time and the equation for free fall, we can find the altitude above the pond.

First, we calculate the time it takes for the package to reach the target location:

  1. Horizontal distance = 521 m
  2. Ground speed = 59.1 m/s
  3. Time = Horizontal distance / Ground speed = 521 m / 59.1 m/s = 8.81 s

Next, we use the equation for free fall to find the altitude above the pond:

  1. Acceleration due to gravity, g = 9.8 m/s^2 (assuming no air resistance)
  2. Time for free fall, t = 8.81 s
  3. Altitude above the pond = 0.5 * g * t^2 = 0.5 * 9.8 m/s^2 * (8.81 s)^2 = 194.89 m

Therefore, the plane must be flying at an altitude of approximately 194.89 m above the pond in order to successfully accomplish this feat.

Learn more about altitude above the pond here:

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