Final answer:
The rate of 126 miles per hour converts to 184.8 feet per second, and at this rate, the parachutist will fall 1848 feet during 10 seconds of free-fall. Opening the parachute slows the fall significantly due to air resistance.
Step-by-step explanation:
To convert the parachutist's rate of 126 miles per hour to feet per second, we start by recognizing that there are 5280 feet in one mile and 3600 seconds in one hour. Converting miles to feet and then dividing by the number of seconds gives:
126 miles/hour × 5280 feet/mile × 1 hour/3600 seconds = 184.8 feet/second
Therefore, the rate in feet per second is 184.8 feet/second.
To determine how far the parachutist will fall in 10 seconds, we simply multiply the rate by the time:
184.8 feet/second × 10 seconds = 1848 feet
So, the parachutist will fall 1848 feet in 10 seconds of free-fall.
Discussing the forces acting on a parachutist, after 2 seconds of free fall, the parachutist accelerates at 9.8 m/s² due to gravity, which gives the initial speed :
Speed = Acceleration × Time = 9.8 m/s² × 2s = 19.6 m/s
After opening the parachute, there is a net upward force due to air resistance, which significantly slows down the fall. This change in dynamics is crucial to ensure the safe landing of the skydiver.
In summary, while the initial rate of freefall is one factor, the ultimate speed at which a parachutist will fall is influenced by factors such as drag, body position, and whether the parachute is open or closed.