An Alaskan rescue plane traveling 43 m/s

drops a package of emergency rations from
a height of 129 m to a stranded party of
explorers.
The acceleration of gravity is 9.8 m/s
2
.
Where does the package strike the ground
relative to the point directly below where it
was released?
Answer in units of m.

time to fall 129m

h=1/2 g t^2
timetofall=sqrt(2*129/9.8)

distance horizontal=43m/s*timetofall

To find where the package strikes the ground relative to the point directly below where it was released, we need to determine the time it takes for the package to hit the ground. Once we know the time, we can calculate the horizontal distance the plane travels in that time.

Step 1: Find the time it takes for the package to reach the ground.
We can use the equations of motion to find the time it takes for the package to fall:

Assuming the initial vertical displacement is -129 m (since it is below the point of release), the acceleration is -9.8 m/s^2, and the final vertical displacement is 0:

Δy = v0 * t + (1/2) * a * t^2

0 = 0 + (1/2) * (-9.8) * t^2

Solving for t gives us: t = sqrt((2 * -129) / -9.8)

Step 2: Calculate the horizontal distance traveled by the plane.
Since the plane is traveling at a constant velocity of 43 m/s, we can use the equation:

d = v * t

where d is the horizontal distance traveled by the plane, v is the velocity, and t is the time calculated in step 1.

Now we can plug in the values and calculate d:

d = 43 m/s * t

Finally, to find where the package strikes the ground relative to the point directly below where it was released, we subtract the horizontal distance traveled by the plane from the initial point of release, which is 0:

Final position = 0 - d

Plug in the calculated value of d to find the final position relative to the point directly below:

Final position = -d

Calculating the answer:

1. Calculate the time:
t = sqrt((2 * -129) / -9.8)
t ≈ sqrt(26.32)
t ≈ 5.13 seconds

2. Calculate the horizontal distance traveled by the plane:
d = 43 m/s * 5.13 s
d ≈ 220.59 meters

3. Calculate the final position relative to the point directly below:
Final position = -220.59 meters

Therefore, the package strikes the ground approximately 220.59 meters from the point directly below where it was released.