An airplane pilot falls 355 m after jumping from an aircraft without his parachute opening. Fortunately, he lands in a snowbank, creating a crater 1.5 m deep, and survives with only minor injuries. Assuming the pilot's mass is 77 kg and his terminal (maximum) velocity while falling is 50 m/s, estimate the following:
a) The work done by the snow in bringing him to the rest
b) The average force exerted on him by the snow to stop him.
c) The work done on him by the air resistance as he fell.
I'm stumped and need some help.
The problem I'm having (in general with Physics) is knowing which equation to use. I used the air resistance force = mg, and the answer came out wrong. So I just don't know what I'm doing wrong.
The problem I'm having (in general with Physics) is knowing which equation to use. I used the air resistance force = mg, and the answer came out wrong. So I just don't know what I'm doing wrong.
To solve these problems, we will make use of different formulas and principles of physics. Let's break down each part of the question and go step by step.
a) The work done by the snow in bringing him to rest:
Work done is given by the formula: Work = Force x Distance. In this case, the force is the weight of the pilot, which can be calculated using the formula: Weight = Mass x Gravity, where gravity is approximately 9.8 m/s².
So, the weight of the pilot is: Weight = 77 kg x 9.8 m/s² = 754.6 N.
Since work is equal to the force applied multiplied by the distance covered, we can find the work done by the snow using the following formula: Work = Force x Distance. The force here is equal to the weight of the pilot, and the distance is the depth of the crater, which is given as 1.5 m.
So, the work done by the snow is: Work = 754.6 N x 1.5 m = 1131.9 J (Joules).
Therefore, the work done by the snow in bringing him to rest is approximately 1131.9 Joules.
b) The average force exerted on him by the snow to stop him:
To find the average force exerted on him, we can use the formula: Average Force = Work / Distance.
In this case, the work done by the snow (from part a) is 1131.9 J, and the distance is 1.5 m (the depth of the crater).
So, the average force exerted on him by the snow is: Average Force = 1131.9 J / 1.5 m = 754.6 N.
Therefore, the average force exerted on him by the snow to stop him is approximately 754.6 Newtons.
c) The work done on him by the air resistance as he fell:
The work done on an object by air resistance can be calculated using the formula: Work = Force x Distance.
In this case, the force of air resistance can be calculated using the formula: Force = (1/2) x Air Density x Velocity² x Surface Area x Drag Coefficient.
The air density varies depending on altitude, temperature, and humidity, but we can approximate it as 1.2 kg/m³.
The velocity is given as the terminal velocity, which is 50 m/s.
The surface area and drag coefficient of a human body in freefall are difficult to determine accurately, but we will assume an average value of 1 m² for surface area and 1 for the drag coefficient.
Using these values, we can calculate the force of air resistance:
Force = (1/2) x 1.2 kg/m³ x 50 m/s² x 1 m² x 1 = 30 N.
Since we know the force and the distance fallen (355 m), we can calculate the work done by air resistance:
Work = Force x Distance = 30 N x 355 m = 10,650 J (Joules).
Therefore, the work done on the pilot by air resistance as he fell is approximately 10,650 Joules.
I hope this helps! Let me know if you have any further questions.
work done=KE at terminal velocity
avearage force*distance=work done
air resistance force=mg
work done by averge resistance force=height falling=mgh-finalKE