Hi all.
I am working on a problem in which I want to model the collision of a moving object, with mass m1, with a stationary base. I have calculated the velocity of the moving object at the instant of collision. I want to model this collision using a mass spring system with damping.
My...
Homework Statement
V is a subspace of Rn and S={v1,...,vk} is a set of linearly independent vector in V. I have to prove that any list of linearly independent vectors can be extended to a basis for V.
Homework Equations
None that I can think of.
The Attempt at a Solution
So to be...
Thanks for your help. I worked out part 1, but I'm still unsure on part 2. For proving the law for a natural number I did:
Let y=ln(a), for a>0,
ey=a, and if we raise each side to the power n we get:
(ey)n=an
ln(ey*n)=ln(an)
y*n = ln(an), but y = ln(a)
n*ln(a) = ln(an)
So I'm still...
Homework Statement
There are two log properties that I have to prove:
1) Explain why ln(b1/n)=(1/n)ln(b) for b>0, set b=an
2) Explain why ln(ar)=rln(a) for any r in Q and a>0, ie r is rational.
Homework Equations
ln(an)=nln(a)
The Attempt at a Solution
In a previous question...
Homework Statement
The question is to use upper and lowers sums, Un and Ln, on a regular petition of the intervals to find the integral from 1 to 2 of f(x) = [[x]], where [[x]] is the greatest integer function.
Homework Equations
\Deltax = \frac{b-a}{n}
The Attempt at a Solution
\Deltax =...
Homework Statement
There is an elliptical path and pegs A and B are restricted to move around it. If the link moves with a constant speed of 10m/s, determine the magnitude of velocity when x=0.6m
[PLAIN]http://users.adam.com.au/shortround/Prob.12-78.jpg [Broken]
Homework Equations...
In my textbook they have an example where the initial velocity is 24m/s and they give the answer as \theta=24.8o below the horizontal and \theta=85.1o above the horizontal.
Okay using v^2 = v_0^2 + 2 a \Delta x I found the final velocity in the y direction to be...
I understand that the initial horizontal velocity is 28cos\theta and the vertical component is 28sin\theta.
As iraten said I could then substitute it into
v^2 = v_0^2 + 2 a \Delta x
, but we do not know the final velocity when the water hits the wall. In the horizontal direction a=0...
Homework Statement
The question is: A fireman at point A wishes to put out a fire at B. Determine the two possible angles \theta1 and \theta2 at which this can be done. The water flows from the hose at vA=28m/s and the value for gravity is 9.81m/s2...