Calculating Maximum Height of a Projectile in Fluid Resistance Problem

In summary, the conversation discusses a small rock moving in water and the force exerted on it by the water, given by the equation Fd = kv. The terminal speed of the rock is found to be 2.0m/s and it is projected upward at an initial speed of 6.0m/s. The task is to find the maximum height the rock reaches, using a differential equation and finding the constant k in terms of terminal velocity and other relevant constants.
  • #1
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Homework Statement


A small rock moves in water, and the force (fluid resistance) exerted on it by the water is given by the equation Fd = kv, where k is a constant. The terminal speed of the rock is measured and found to be 2.0m/s. The rock is projected upward at an initial speed of 6.0m/s. You can ignore the buoyancy force on the rock. Find the maximum height that the rock reaches.

I'm not quite sure if there is enough information given to actually solve this question. I can't seem to figure out how to start the question either :(
 
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  • #2
There's enough information. You have to construct and solve a differential equation for the motion of the rock as it rises. Start by finding an expression for the constant k in terms of the terminal velocity and any other relevant constants.
 

FAQ: Calculating Maximum Height of a Projectile in Fluid Resistance Problem

What is fluid resistance?

Fluid resistance is a force that opposes the motion of an object through a fluid, such as air or water. It is caused by the friction between the fluid and the surface of the object.

How is fluid resistance calculated?

The calculation of fluid resistance depends on various factors such as the size and shape of the object, the density and viscosity of the fluid, and the velocity of the object. It is typically calculated using equations derived from fluid dynamics principles.

What are some practical applications of fluid resistance?

Fluid resistance is an important factor in various industries such as aerospace, automotive, and marine. It is also crucial in sports equipment design, as well as the design of buildings and structures to withstand wind forces.

How can fluid resistance be reduced?

One way to reduce fluid resistance is by streamlining the shape of an object to minimize its surface area and create a more aerodynamic or hydrodynamic design. Other methods include using smooth surfaces, reducing the speed of the object, or using special coatings to reduce friction.

What is the difference between drag and lift in terms of fluid resistance?

Drag is the component of fluid resistance that acts in the opposite direction of the object's motion, while lift is the component that acts perpendicular to the object's motion. In other words, drag slows down the object, while lift may help it move in a different direction or stay afloat in a fluid. Both forces are important to consider in fluid resistance problems.

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