Question

Hi, can someone please help me with this report? It doesn't have to be like an essay, even two paragraphs is great. Please I really need help with this and really need it done. thank you so much!

The U.S. Army is planning to drop supplies from a plane at a refugee camp. The supplies are divided into 700-kilogram parcels, and the parachutes have an area of 100 square meters. The only problem is that the parcels cannot hit the ground at a velocity of more than 5 meters per second without damaging the contents. Are these parachutes suitable for this task?

For the purposes of this exercise, assume that the for the drag coefficient of the parachute is 1.5 and that the air density is 1.22 kilograms per cubic meter. Write a report detailing why these parachutes are or are not suitable and determining the minimum size parachute that can be used in this situation.

Answer 1

The U.S. Army is planning to drop 700-kilogram parcels of supplies to a refugee camp using parachutes with an area of 100 square meters. The objective is to prevent the parcels from hitting the ground at a velocity of more than 5 meters per second to avoid damage to the contents. To determine the suitability of these parachutes, we need to consider the drag coefficient and the air density.

Using the formula for air resistance, we can calculate the force acting on the parachute:

Force = 0.5 x Drag Coefficient x Air Density x Velocity^2 x Area

Assuming that the terminal velocity of the parcels is 5 meters per second, we can calculate the force acting on the parachute as follows:

Force = 0.5 x 1.5 x 1.22 x 5^2 x 100
= 1822.5 N

The weight of the parcels is 700 kg x 9.8 m/s^2 = 6860 N. Therefore, the force acting on the parachute is much less than the weight of the parcels, indicating that the parachutes are suitable for this task.

To determine the minimum size parachute that can be used in this situation, we need to calculate the maximum weight that can be supported by a parachute with an area of 100 square meters. This is known as the payload capacity of the parachute and can be calculated as follows:

Payload Capacity = Area x Drag Coefficient x Air Density x Velocity^2 / 2 x 9.8

Assuming that the maximum weight of the parcels that can be dropped is 700 kg, we can solve for the minimum size parachute as follows:

100 x 1.5 x 1.22 x 5^2 / (2 x 9.8) = 240.9 kg

Therefore, the minimum size parachute required for dropping 700-kilogram parcels at a velocity of less than 5 meters per second is approximately 241 square meters. In conclusion, the 100 square meter parachutes are suitable for this task, and a larger parachute would be required if the weight of the parcels increased.

Answer 2

Introduction:

In this report, we will examine whether the 100 square meter parachutes with a drag coefficient of 1.5 are suitable for dropping 700-kilogram parcels from a plane at a refugee camp. The main concern is that the parcels cannot hit the ground at a velocity of more than 5 meters per second without damaging the contents.

Calculation:

To determine whether the 100 square meter parachutes with a drag coefficient of 1.5 are suitable, we need to calculate the terminal velocity of the parcels. The terminal velocity is the maximum velocity that the parcels can reach when they are falling through the air. We can calculate the terminal velocity using the following equation:

Vt = sqrt((2mg)/(ρACd))

Where:

Vt is the terminal velocity

m is the mass of the parcel (700 kg)

g is the acceleration due to gravity (9.8 m/s^2)

ρ is the air density (1.22 kg/m^3)

A is the area of the parachute (100 m^2)

Cd is the drag coefficient (1.5)

Substituting these values into the equation, we get:

Vt = sqrt((2 x 700 x 9.8)/(1.22 x 100 x 1.5)) = 52.0 m/s

This means that without any parachute, the parcel would hit the ground with a velocity of 52 m/s. However, the parachutes are designed to provide air resistance, which will slow down the parcels.

To determine whether the parachutes are suitable, we need to calculate the velocity at which the parcels will hit the ground when they are attached to the parachutes. We can use the following equation to calculate the force of air resistance:

F = (1/2)ρAv^2Cd

Where:

F is the force of air resistance

ρ is the air density (1.22 kg/m^3)

A is the area of the parachute (100 m^2)

v is the velocity of the parcel

Cd is the drag coefficient (1.5)

When the force of air resistance is equal to the weight of the parcel, the parcel will stop accelerating and will reach its terminal velocity. Therefore, we can set the force of air resistance equal to the weight of the parcel:

F = mg

Substituting the values into the equation, we get:

(1/2)ρAv^2Cd = mg

Solving for v, we get:

v = sqrt((2mg)/(ρACd))

Substituting the values into the equation, we get:

v = sqrt((2 x 700 x 9.8)/(1.22 x 100 x 1.5)) = 25.9 m/s

This means that the velocity at which the parcels will hit the ground when they are attached to the parachutes is 25.9 m/s.

Conclusion:

Based on our calculation, the 100 square meter parachutes with a drag coefficient of 1.5 are suitable for dropping 700-kilogram parcels from a plane at a refugee camp. The velocity at which the parcels will hit the ground when they are attached to the parachutes is 25.9 m/s, which is below the maximum velocity of 5 m/s specified by the U.S. Army. However, if the mass of the parcels or the area of the parachutes changes, the velocity at which the parcels hit the ground will also change. Therefore, it is important to recalculate the velocity for different scenarios to ensure the safety of the parcels.

Step-by-step explanation: