Calculating a Gentle Landing for a Skydiver: Solving for Time and Height

In summary, the skydiver falls for a total of 3 seconds. During the free fall portion of the jump, there is essentially no air resistance, so the force is F = −mg. After the parachute opens, a significant drag term due to the air resistance of the parachute affects the force, causing the force to become F = −mg − kv.
  • #1
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This is my 3rd practice question that I don't know how to do :( Hoping peole can help me out, if someone could even work it out, would be greatly appriciated.

A skydiver, weighing 70kg, jumps from an aeroplane at an
altitude of 700 metres and falls for T1 seconds before pulling
the rip cord of his parachute. A landing is said to gentle if
the velocity on impact is no more than the impact velocity of
an object dropped from a height of 6 metres. The distance

that the skydiver falls during t seconds can be found from New-
ton’s Second Law, F = ma. During the free fall portion of
the the jump, we will assume that there is essentially no air
resistance, so F = −mg where g = 9.8ms^−2 and m = 70kg.
After the parachute opens, a significant drag term due to the
air resistance of the parachute affects the force F, causing the
force to become F = −mg − kv where v is the velocity and
k = 110kg/sec is a drag coefficient.

(a) Find the range of times T1 at which the rip cord can be
pulled for a gentle landing.

(b) Find the height after T1 seconds of free-fall.
 
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  • #2
You've given a pretty detailed explanation of HOW to do the problem- all that's missing is writing down the approriate formulas and then doing the arithmetic.

How is distance fallen related to acceleration in free fall?

What is the total force on the skydiver after the the parachute opens?

More than that we can't say until you show us what you have tried and what knowledge you have. If you can do differential equations, this is pretty straightforward. If not, then you would have to have been given appropriate formulas relating force, acceleration, speed, and distance. What formulas do you have?
 
  • #3
Well we got this in maths. And we have studied DE's. I also study physics. So pick your method / formulas.

If I solved what v is how would that help me ?
 
  • #4
If you solve for v and d for the diver in free fall (as a function of t of course), then you know how fast he is going and how high he is when his parachute opens (t1). Using those as initial values, you can solve for his speed and height at any time t after the parachute opens. Then find his speed when he hits the ground (what do you consider a "gentle landing"?) and any time t.
 
  • #5
Is an analytical solution possible? When I find an equation for T1 it includes exponential as well as polynomial terms... It seems like you need to graph it to solve for T1.
 
  • #6
learningphysics, I think you're right about the graph to find the possible values.

I'll see what I can do, damn taugh question for me
 
  • #7
Solved the question, thanks for the replies
 

FAQ: Calculating a Gentle Landing for a Skydiver: Solving for Time and Height

How does air resistance affect a skydiver's speed?

Air resistance, also known as drag, is a force that acts in the opposite direction of an object's motion through the air. As a skydiver falls, air resistance increases and eventually balances out the force of gravity, causing the skydiver to reach a constant speed known as terminal velocity.

How does a skydiver's weight affect their acceleration?

According to Newton's second law of motion, the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. Therefore, a skydiver with a greater weight will experience a larger force of gravity and therefore a greater acceleration towards the ground.

What is the difference between freefall and skydiving?

Freefall refers to the state of falling through the air without any external forces acting on an object. Skydiving, on the other hand, involves jumping from a high altitude and using a parachute to slow down and control the descent. During skydiving, the skydiver experiences freefall until the parachute is deployed.

How does air density affect a skydiver's descent?

Air density, which is affected by factors such as altitude and temperature, can impact a skydiver's descent by altering the amount of air resistance they experience. In denser air, there is more air resistance, causing the skydiver to fall at a slower speed. In less dense air, there is less air resistance, resulting in a faster descent.

What is the importance of a parachute in skydiving?

A parachute is essential in skydiving as it allows the skydiver to control their descent and safely land on the ground. The parachute increases air resistance, slowing down the skydiver's fall and allowing them to safely land on the ground. Without a parachute, a skydiver would reach a dangerously high speed and could potentially be injured upon impact with the ground.

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