## How to Calculate Average Speed Skydiver Parachute
When a skydiver jumps from a plane, they experience two distinct phases of motion: freefall and parachuting. During freefall, the skydiver accelerates due to gravity, while during parachuting, the skydiver’s speed is reduced by the drag force of the parachute. The average speed of a skydiver during the entire jump can be calculated by taking into account both the freefall and parachuting phases.
### Freefall Phase
During freefall, the skydiver’s speed increases until they reach terminal velocity. Terminal velocity is the maximum speed that a skydiver can achieve in freefall, and it depends on the skydiver’s body weight, shape, and orientation. The terminal velocity for a typical skydiver is about 120 mph (193 km/h).
The distance traveled by the skydiver during freefall is given by:
“`
distance = 1/2 acceleration time^2
“`
where:
acceleration is the acceleration due to gravity (9.8 m/s^2)
time is the time spent in freefall
The time spent in freefall can be calculated by dividing the distance traveled by the terminal velocity:
“`
time = distance / terminal velocity
“`
### Parachuting Phase
Once the skydiver deploys their parachute, the drag force of the parachute slows them down. The drag force depends on the size and shape of the parachute, as well as the speed of the skydiver.
The average speed of the skydiver during the parachuting phase can be calculated by using the following formula:
“`
average speed = (distance / time) (1 / 2)
“`
where:
distance is the distance traveled during the parachuting phase
time is the time spent in the parachuting phase
The time spent in the parachuting phase can be calculated by dividing the distance traveled by the average speed:
“`
time = distance / average speed
“`
### Average Speed of the Entire Jump
The average speed of the skydiver during the entire jump can be calculated by taking into account both the freefall and parachuting phases. The average speed is given by:
“`
average speed = (distance / time) (1 / 2)
“`
where:
distance is the total distance traveled during the jump
time is the total time spent in the jump
The total distance traveled during the jump is the sum of the distance traveled during freefall and the distance traveled during parachuting. The total time spent in the jump is the sum of the time spent in freefall and the time spent in parachuting.
### Example Calculation
Let’s say that a skydiver jumps from a plane at an altitude of 10,000 feet (3,048 meters). The skydiver falls in freefall for 10 seconds before deploying their parachute. The parachute slows the skydiver down to an average speed of 10 mph (16 km/h). The skydiver lands on the ground after a total time of 60 seconds.
The distance traveled during freefall is:
“`
distance = 1/2 acceleration time^2
distance = 1/2 9.8 m/s^2 (10 s)^2
distance = 490 meters
“`
The distance traveled during parachuting is:
“`
distance = average speed time
distance = 10 mph (60 s – 10 s)
distance = 500 meters
“`
The total distance traveled during the jump is:
“`
distance = distance during freefall + distance during parachuting
distance = 490 meters + 500 meters
distance = 990 meters
“`
The total time spent in the jump is:
“`
time = time during freefall + time during parachuting
time = 10 s + (500 meters / 10 mph)
time = 60 s
“`
The average speed of the skydiver during the entire jump is:
“`
average speed = (distance / time) (1 / 2)
average speed = (990 meters / 60 s) (1 / 2)
average speed = 8.25 m/s
“`
Therefore, the average speed of the skydiver during the entire jump is 8.25 m/s, or about 18.4 mph (29.6 km/h).
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