Calculating Drag Force on Boat: Speed as Function of Time

In summary, drag force is the resistance force that acts against a moving object through a fluid, such as air or water. In the context of a boat, drag force is the force that acts against the boat as it moves through water, slowing it down. It can be calculated using the equation Fd = 0.5 * p * v^2 * Cd * A, and it causes a boat's speed to decrease over time. Some factors that can affect drag force on a boat include the size and shape of the boat, the speed and density of the water, and external forces such as wind or waves. To minimize drag force, it is important to consider factors such as the boat's design, materials, and speed, as
  • #1
datapirate42
1
0
F = -kv2

A fishing boat of mass m moves through the water in the +x direction. At time = 0 and x=0 it shuts its engines off and begins to drift. It experiences drag according to the above equation, calculate the boat's speed as a function of time.

I've tried taking F = ma
so a = -kv2/m

now v should be the integral of that with respect to time
my problem is getting v as a function of t without it being in that function itself
 
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  • #2
Hint: Replace a with its equivalent dv/dt.
 

Related to Calculating Drag Force on Boat: Speed as Function of Time

1. What is drag force and how does it affect a boat's speed?

Drag force is the resistance force that acts against a moving object through a fluid, such as air or water. In the context of a boat, drag force is the force that acts against the boat as it moves through water, slowing it down. The higher the drag force, the slower the boat will be.

2. How is drag force calculated on a boat?

The drag force on a boat can be calculated using the equation Fd = 0.5 * p * v^2 * Cd * A, where Fd is the drag force, p is the density of the fluid, v is the velocity of the boat, Cd is the drag coefficient, and A is the cross-sectional area of the boat.

3. How does the speed of a boat change over time due to drag force?

As a boat moves through water, drag force will act against it, causing it to slow down. This means that the boat's speed will decrease over time as it continues to face resistance from drag force. The rate at which the boat slows down will depend on factors such as the shape and size of the boat, as well as the speed and density of the water.

4. What are some factors that can affect drag force on a boat?

Some factors that can affect drag force on a boat include the size and shape of the boat, the speed at which it is moving, the density and viscosity of the water, and any external forces acting on the boat, such as wind or waves. Additionally, the design and materials of the boat can also play a role in the amount of drag force it experiences.

5. How can drag force be minimized on a boat?

To minimize drag force on a boat, it is important to consider factors such as the boat's design, materials, and speed. A streamlined and lightweight boat can reduce the amount of drag force it experiences. Additionally, maintaining a constant and efficient speed can also help minimize drag force, as sudden changes in speed can increase drag. Regular maintenance and cleaning of the boat's hull can also help reduce drag force.

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