The drag is proportional to the square of the speed of the boat, in the form Fd=bv2 where b= 0.5 N⋅ s2/m2. What is the acceleration of the boat just after the rain starts? Take the positive x axis along the direction of motion.

The first part of the question is missing and it is:

A boat of mass 250 kg is coasting, with its engine in neutral, through the water at speed 3.00 m/s when it starts to rain. The rain is falling vertically, and it accumulates in the boat at the rate of 10.0 kg/hr.

a(o) = 18.03 x 10^(-3) m/s^(-2)

Explanation:

First of all, if we make a momentum balance in the direction of motion (the x-direction), we'll discover that the change of the momentum will be equal to the forces acting on the boat.

Hence, there is only the drag force, which acts against the direction of motion as:

d(m·v)/dt = - k·v² (since f_d = - k·v²)

where k = 0.5 Ns²/m²

Now let's simplify the time derivative on the Left, by applying product rule of differentiation and we obtain:

v·dm/dt + m·dv/dt = - k·v²

where dm/dt = 10kg/hr (this is the change of the mass of the boat)

Furthermore, acceleration is the time derivative of time velocity, Thus;

a = dv/dt = - (k·v² + v·dm/dt) / m

Now, for the moment,when the rain starts; since we know all the values on the right hand side, let's solve for the acceleration ;

a(o) = - (ko·vo² + vo·dm/dt) / mo

= -[ (0.5(3)²) + (3x10/3600)/250

(dt = 3600secs because 1hr = 3600 secs)

So a(o) = 18.03 x 10^(-3) m/s^(-2)

carbon is found in all living things. carbon atoms move constantly through

living organisms, the oceans, the atmosphere, and the earth’s crust in what is

known as the carbon cycle. the directions taken by carbon atoms through this

cycle are very complicated and can take millions of years to make a full circle.

all animals, from humans to the dinosaurs are part of the carbon cycle. when

animals eat food, they get carbon in the form of carbohydrates and proteins.

in animals, oxygen combines with food in the cells to produce energy for daily

activity and then gives off carbon. the carbon combines with oxygen to form

carbon dioxide (co2) and is released back into the atmosphere as a waste

product when animals breathe and exhale.

from 145-65 million years ago, earth was much

hotter than today and covered with dense,

tropical swamp forests. the trees and other

plants were immense and

provided an endless supply of

food for the giant animals that

roamed the land. somewhere in

the air above one of these

forests, a lone carbon atom has joined

up with two oxygen atoms to form a molecule of co2.

the co2 molecule was sucked into the tiny holes (stomata) on the leaf of a

fern plant and joined with sunlight, chlorophyll and water to make food and

energy in the plant’s cells through photosynthesis. the oxygen (o2) from the

co2 molecule was sent back into the atmosphere; the carbon atom (c) was

detached and used to make a molecule of sugar.

if that carbon atom had been eaten instead, a totally

different situation would have developed. let’s say

that a giant plant-eating dinosaur (herbivore) ate the

fern for breakfast, and swallowed the carbon in the

fern in the form of carbohydrates and proteins. in

the process of respiration, oxygen combined with

the carbohydrates and proteins in the dinosaur’s cells

to provide energy for its daily activity.  

falling water hydro = water .. spectcular places these plants are