Calculating speed in water taking drag force into account

In summary, the problem is to determine how long it takes a person with a mass of 75 kg and a speed of 6.5 m/s to reach 2% of their original speed while diving into a pool with a drag force of Fd = (−1.00×104 kg/s) v. To solve this, we need to use Newton's second law and solve a differential equation for velocity as a function of time, taking into account gravity.
  • #1
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Homework Statement



You dive straight down into a pool of water. You hit the water with a speed of 6.5 m/s, and your mass is 75 kg. Assuming a drag force of the form Fd = (−1.00×104 kg/s) v, how long does it take you to reach 2% of your original speed? (Ignore any effects of buoyancy.)

Homework Equations



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The Attempt at a Solution



no ideas whatsoever
 
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  • #2
First, write down Newton's second law. On one side we have acceleration, which is the first derivative of velocity, and on the other side, we have velocity, so this is a differential equation. (Don't forget about gravity.) Solve this differential equation to get velocity as a function of time. This should get you started.
 

Related to Calculating speed in water taking drag force into account

1. How does drag force affect the speed of an object in water?

Drag force is a resistance force that acts in the opposite direction of an object's motion through a fluid, such as water. It increases as the speed of the object increases, ultimately limiting the maximum speed an object can achieve.

2. What is the formula for calculating speed in water with drag force?

The formula for calculating speed in water with drag force is: v = (mg/k)^1/2 * (1 - e^(-kt/m)), where v is the speed, m is the mass of the object, g is the acceleration due to gravity, k is the drag coefficient, and t is the time.

3. How do you determine the drag coefficient for an object in water?

The drag coefficient for an object in water depends on its shape, size, and surface roughness. It can be determined experimentally by measuring the drag force at different speeds and using the formula CD = Fd/ (1/2 * p * v^2 * A), where CD is the drag coefficient, Fd is the drag force, p is the density of water, v is the speed, and A is the frontal area of the object.

4. Is there a way to reduce drag force and increase speed in water?

Yes, there are several ways to reduce drag force and increase speed in water. One way is to reduce the frontal area of the object, such as by making it more streamlined. Another way is to use a smoother surface or add a coating that reduces friction. Additionally, increasing the speed of the water flow around the object can also reduce drag force and increase speed.

5. How does the density of water affect the speed of an object in water?

The density of water does not directly affect the speed of an object in water. However, it does indirectly affect the drag force, as the drag force is dependent on the density of the fluid. Objects will experience more drag force in denser fluids, thus limiting their speed.

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