# Boat Drag Question: Acceleration After Rain Starts

• vpea
In summary, ~~-The boat experiences a negative acceleration due to the drag force applied by the water.
vpea
A boat of mass 250kg is coasting, with its engine in neutral, through the water at speed 3.00m/s when it starts to rain. The rain is falling vertically, and it accumulates in the boat at the rate of 10.0kg/hr. Assume that the boat is subject to a drag force due to water resistance. The drag is proportional to the square of the speed of the boat, in the form F=0.5v^2. What is the acceleration of the boat just after the rain starts?

I've been approaching this question from a few angles and don't seem to be getting anywhere. I found the answer to the 1st part using conservation of momentum, but since momentum is no longer conserved I don't know what to do. I'd really appreciate some help with this.

$$a = \frac{0.5v^2}{m}$$

But I don't see how you could use the other problem data.

vpea said:
A boat of mass 250kg is coasting, with its engine in neutral, through the water at speed 3.00m/s when it starts to rain. The rain is falling vertically, and it accumulates in the boat at the rate of 10.0kg/hr. Assume that the boat is subject to a drag force due to water resistance. The drag is proportional to the square of the speed of the boat, in the form F=0.5v^2. What is the acceleration of the boat just after the rain starts?

I've been approaching this question from a few angles and don't seem to be getting anywhere. I found the answer to the 1st part using conservation of momentum, but since momentum is no longer conserved I don't know what to do. I'd really appreciate some help with this.
SOLUTION HINTS:
{Rain Accumulation Rate} = (10.0 kg/hr) = (2.7778e(-3) kg/sec)
{Horizontal Boat Speed} = (3.00 m/s)

From Conservation of Momentum between Boat and Rain Drops:
{Change in Boat's Horizontal Momentum DUE TO RAIN ACCUMULATION} =
= -{Change in Rain's Horizontal Momentum when Accumulating in Boat}

::: ⇒ -{FORCE on Boat from Rain Accumulation} = Frain =
= -{RATE OF CHANGE in Boat's Horizontal Momentum DUE TO RAIN ACCUMULATION} =
= {RATE OF CHANGE in Rain's Horizontal Momentum when Accumulating in Boat} =
= {Rain Accumulation Rate}*{Horizontal Boat Speed} =
= (2.7778e(-3) kg/sec)*(3.00 m/s) =
= (8.3334e(-3) N)

{Acceleration of Boat} = {Net Force on Boat}/{Mass of Boat} =
= {-(Drag Force) - (Frain)}/{Mass of Boat}
= {-0.5v^2 - (Frain)}/{Mass of Boat} =
= { (-0.5)*(3.00 m/s)^2 - (Frain) }/{Mass of Boat} =
Determine boat acceleration (negative because boat is slowing) from this last equation using values given and/or computed previously.

~~

Last edited:

## 1. What is boat drag?

Boat drag is the resistance or force exerted on a boat as it moves through the water. It is caused by the friction between the boat's hull and the water, as well as other factors such as the shape and weight of the boat.

## 2. How does rain affect boat drag?

Rain can increase boat drag due to the added weight and surface tension of the raindrops on the boat's hull. This can slow down the boat and make it more difficult to accelerate.

## 3. Why does acceleration decrease after rain starts?

Acceleration decreases after rain starts because the added drag from the rain makes it harder for the boat to move through the water. This can also be affected by the type of boat and the speed at which it is traveling.

## 4. Can boat drag be reduced in rainy conditions?

Yes, boat drag can be reduced in rainy conditions by using techniques such as waxing the hull to reduce surface tension, adjusting the boat's trim to minimize drag, and using a more aerodynamic boat design.

## 5. How does boat speed affect drag in rainy conditions?

The faster a boat is traveling, the more drag it will experience in rainy conditions. This is due to the increased force of the raindrops hitting the boat's hull at higher speeds. Therefore, it may be more difficult to maintain high speeds in rainy conditions.

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