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.