# Helicopter Problem: Dropping an Inflatable Raft

• Rowie25
In summary, the problem involves a helicopter dropping an inflatable raft to flood victims while flying at a velocity of 10 m/s at an angle of 30 degrees below the horizontal. Neglecting air resistance, the time it takes for the raft to land is approximately 1.86 seconds and it will land 15.8 meters away from the victims. To find the location of the helicopter when the package lands, further information or equations are needed.
Rowie25

## Homework Statement

A helicopter drops an inflatable raft to flood victims floating in a lake. When the raft is released the helicopter is 50 m directly above the victims and flying at a velocity of 10 m/s at an angle of 30 degrees below the horizontal. Neglect air resistance.
a. How long is the package in the air?
b. How far from the victims does the raft land?
c. Assuming the helicopter drops the package at coordinates (0,0). If the helicopter continues to fly at a constant velocity, where is the helicopter when the package lands?

I think the fact that the helicopter is moving is confusing me. Wouldn't you use the formula y=y_o+v_oysin(angle)(t)-(1/2)gt^2 ?? So you find the time? And then you could use v_y=v_oy-gt to find the velocity? I am not sure how to find c. Please help!

Homework Equationsy=y_o+v_oysin(angle)(t)-(1/2)gt^2 v_y=v_oy-gt The Attempt at a Solution To find a, use the equation y=y_o+v_oysin(angle)(t)-(1/2)gt^2 50=0+10sin30(t)-(1/2)(-9.8)t^2 t=1.86 s To find b, use the equation x=x_o+v_oxcos(angle)t x=0+10cos30t x=15.8 m To find c, I am confused.

I can assist in answering the questions posed in this helicopter problem.
a. To find the time the package is in the air, we can use the formula for vertical displacement: y = y0 + v0yt - 1/2gt^2. Since the initial vertical position (y0) is 50m and the initial vertical velocity (v0y) is 10m/s, we can plug in these values and solve for t. This gives us a time of approximately 3.19 seconds.
b. To find the distance from the victims that the raft lands, we can use the formula for horizontal displacement: x = x0 + v0xt. Since the initial horizontal position (x0) is 0m and the initial horizontal velocity (v0x) is 10m/s, we can plug in these values and solve for t. This gives us a distance of approximately 31.9 meters.
c. To find the position of the helicopter when the package lands, we can use the same formula for horizontal displacement and solve for t. This time, we will use the distance from part b as our x value and the velocity of the helicopter (10m/s) as our v0x. This gives us a time of approximately 3.19 seconds. We can then use this time in the formula for vertical displacement to find the vertical position of the helicopter at this time. This will give us a position of (31.9m, 25m) relative to the initial position of (0,0).
I hope this helps in understanding how to approach and solve this problem.

## 1. How does the helicopter drop the inflatable raft?

The helicopter will fly over the designated area and release the raft using a winch system. The winch will slowly lower the raft to the ground while the helicopter maintains a stable position.

## 2. How does the raft inflate once it is dropped?

The raft is equipped with an automatic inflation system that is triggered upon contact with water. The system uses a CO2 cartridge to rapidly inflate the raft, ensuring it is ready for use as soon as it hits the water.

## 3. What factors affect the successful deployment of the inflatable raft?

The main factors that can affect the successful deployment of the inflatable raft include wind speed and direction, altitude of the helicopter, and the weight and size of the raft. It is important for the helicopter pilot to carefully consider these factors before dropping the raft.

## 4. Can the inflatable raft be used multiple times after being dropped?

Most inflatable rafts used in helicopter drops are designed for single-use only. Once the raft has been deployed and inflated, it cannot be deflated and repacked for future use. It is important to have a backup raft in case of multiple emergency situations.

## 5. How long does it take for the raft to fully inflate?

The inflation process for the raft is very quick and typically takes only a few seconds. However, the time it takes for the raft to fully inflate may vary depending on the specific model and environmental conditions. It is important for the helicopter pilot to closely monitor the deployment to ensure the raft is fully inflated and ready for use.

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