An object of mass 80 kg is released from rest from a boat into the water and allowed to sink. While gravity is pulling the object down, a buoyancy force of StartFraction 1 Over 40 EndFraction times the weight of the object is pushing the object up (weight = mg). If we assume that water resistance exerts a force on the object that is proportional to the velocity of the object, with proportionality constant 10 N-sec/m, find the equation of motion of the object. After how many seconds will the velocity of the object be 60 m/sec? Assume that the acceleration due to gravity is 9.81 m divided by sec squared.

Explanation:

Given:

mass of the object,

force of buoyancy acting on the object,

initial velocity of the object,

Given that the water resistance acts on the object is proportional to

So, the net force acting on the object:

.........................................(1)

Now the acceleration of the object can be given as:

From the standard equation of motion:

final velocity

initial velocity

time

.................................(2)

Now the velocity of the object is,

because it says use -2,0,and 2 for x, we can plug those numbers into the equation. y/4=3/4(-2)+2   y/4= -1 1/2 +2 now to get x by itself, we can multiply each side by 4. y=-6+8 which equals y=2 when x=-2. now you can do the same thing with 0 and 2 as x. you get y=8 when x=0 and y=14 when x=2.

x   |   y

-2 |   2

0   |   8

2   |   14

a. are