How Does a Skydiver's Velocity Change with Distance After Parachute Deployment?

In summary, the sky driver reaches a terminal velocity of 373 ms^-1 and deploys his parachute at a height of 1500m. His drag force equals bv^2 and can be ignored. The sky driver finds an expression for velocity as a function of distance traveled from the point the parachute was deployed.
  • #1
Will Freedic
6
0

Homework Statement


A sky driver reaches his terminal velocity of 373 ms^-1 and deploys his parachute at a height of 1500m, the drag force =bv^2 and weigh can be ignored. Find an expression for velocity as a function of distance traveled from the point the parachute was deployed

The Attempt at a Solution


I can find velocity as a function of time easy enough but not a function of distance[/B]
 
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  • #2
Hi Will, :welcome:

Please read the guidelines, use the template, don't delete parts of the template, show your work so far and we'll help you from the point where you get stuck.
 
  • #3
Will Freedic said:

Homework Statement


A sky driver reaches his terminal velocity of 373 ms^-1 and deploys his parachute at a height of 1500m, the drag force =bv^2 and weigh can be ignored. Find an expression for velocity as a function of distance traveled from the point the parachute was deployed
A terminal velocity of 373 m/s is quite a feat. It's also greater than Mach 1, which makes it unlikely to occur. Are you sure a decimal point hasn't been misplaced?
 
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  • #4
There is a standard trick for eliminating time from an acceleration equation.
##a=\frac{dv}{dt}=\frac{dv}{dx}\frac{dx}{dt}=v\frac{dv}{dx}##.
Note that if we apply this to F=ma and integrate wrt x we get ##\int F.dx=\frac 12 mv^2##.
 
  • #5
Thank you!, so is it correct to say that:

Cv2 = ma
cv2 = mv dvdx.
Cm/x = v2 / 2 + c
Cheers
 
  • #6
Will Freedic said:
Thank you!, so is it correct to say that:

Cv2 = ma
cv2 = mv dvdx.
Cm/x = v2 / 2 + c
Cheers
A couple of problems there. First, what happened to gravity? Secondly, I don't understand what you did to get from cv2 = mv dvdx (presumably you meant mv dv/dx) to Cm/x = v2 / 2 + c
 
  • #7
haruspex said:
A couple of problems there. First, what happened to gravity? Secondly, I don't understand what you did to get from cv2 = mv dvdx (presumably you meant mv dv/dx) to Cm/x = v2 / 2 + c
Thank you for your help, i am new to these forums so am a little slow!, managed to get there now tho
 

1. What is drag force and how does it affect a skydiver?

Drag force is a force that opposes the motion of an object through a fluid, such as air. It is caused by the resistance of the fluid to the object's movement. For a skydiver, drag force acts against their downward motion, slowing them down as they fall.

2. How does the shape of a skydiver affect the drag force?

The shape of a skydiver greatly affects the drag force they experience. A more streamlined shape, like a pencil, will experience less drag force than a flat surface, like a sheet of paper. This is because the streamlined shape allows the air to flow smoothly around the object, while the flat surface creates turbulence and increases drag force.

3. Does the speed of the skydiver affect the drag force?

Yes, the speed of the skydiver greatly affects the drag force they experience. As the skydiver falls faster, the drag force increases. This is because the faster they fall, the more air molecules they come into contact with, creating more resistance and thus increasing the drag force.

4. How does the size of a skydiver affect the drag force?

The size of a skydiver also plays a role in the drag force they experience. A larger skydiver will experience more drag force than a smaller skydiver, as they have a larger surface area for the air to push against. This is why skydivers often wear tight-fitting suits to minimize their surface area and reduce drag force.

5. Can a skydiver control their drag force?

Yes, a skydiver can control their drag force to some extent. By changing their body position, they can alter their surface area and thus affect the amount of drag force they experience. For example, spreading their arms and legs wide will increase their surface area and drag force, while tucking their limbs close to their body will decrease it. Additionally, skydivers can use parachutes to further control their descent and drag force.

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