1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Boat Drag question

  1. Apr 11, 2005 #1
    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.
  2. jcsd
  3. Apr 11, 2005 #2
    [tex]a = \frac{0.5v^2}{m}[/tex]

    But I don't see how you could use the other problem data.
  4. Apr 11, 2005 #3


    User Avatar
    Science Advisor

    {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: Apr 11, 2005
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - Boat Drag question Date
Find velocity of boat as function of the time Jun 6, 2017
Speed of a boat Apr 12, 2017
Moving boats with drag force Apr 8, 2015
Drag force on a boat Nov 3, 2010