# falling

1. ### formula of falling object

the original question ism(dv/dt) = mg-kv , after rearranging , i have came to the equation in the picture is there anything wrong with my working in the photo ?
2. ### Data point falling within 3 standard deviations of mean = Significance?

Hi all :) Unfortunately, I'm not a math/stats major but a Chemistry major working on my laboratory reports. I do have a data point/result that lies within 2-3 standard deviations from the mean/expected result. What can I conclude from this? I read that 99.7% of the points fall within 3 SD...
3. ### free falling with resistance

I reviewed the classical problem about an object falling through some medium. Resistance is propotional to the square of speed. Corresponding differential equation is as follows \frac{dv}{dt}=-mg+k v^{2} , with k=2, m=10, g=9.8. In some step of solution \frac{|v+7|}{|v-7|}=ce^{\frac{14}{5}t}...
4. ### The motion of a body falling in a viscous medium differential equation help (:

The motion of a body falling in a viscous medium may be described by the equation: m(dv/dt) = -bv-mg where m, g, b are positive constants. The initial conditions are v(0) = 0 and x(0) = 0.Determine the velocity v(t) and displacement x(t) for t < 0. Anyone able to help please?
5. ### Prob. of falling into a certain interval

Sorry about the poor title. Here are my problems: 1. Divide [0,1] into k intervals of equal size, and generate n observations from a uniform distribution. The number X_i of these n observations which fall into the i:th interval is a random variable. What is the distribution of X_i? 2. Consider...
6. ### velocity of a falling ball help

In our simple model of the fight of a ball, the height y above the foor at time t is y = V_{n}t-\frac{1}{2}gt^{2} where g is the acceleration due to gravity and vn is the velocity immediately after the nth bounce. The maximum height of the ball is reached when dy/dt = 0 Find the time...
7. ### Three tasks regarding falling - did I get them right?

1. A rock was thrown at the angle of 30 degrees against the horizontal surface, being given a velocity V_0=12m/s. Find the largest height h and the Z - the range of the throw. 2. Two rocks are falling from a roof. The second one begins its fall when the first one has already covered 30cm...
8. ### probability of balls falling to bins

Hi everyone, here is my question: Suppose there are "b" balls and n bins, we like to put all balls into "n" bins and the probability that every ball falls into any bin is same(1/n). Is there a simple equation/series of equations to calculate the probability that there are x bins (0<x<=n)...
9. ### falling body

A free falling body has no initial velocity. Its mass is 80kg and the air resistence is proportional to the velocity squared with the proportional constant 0.16kg/m.Let velocity be y m/s and x s. And the question is to put up a differential equation for this. My attempt at the solution. y(0)=0...
10. ### Motion question: Falling object.

2) Problem : You must believe that the coyote is falling at one specific speed at any time during his fall to the ground. Your task here is to find the coyote’s exact speed at each full second of his fall. Once we know this information you can develop a rule that will allow you to find the...
11. ### Motion question: Falling object #2

I have this free falling question and it would be greatly appreciated if someone could help me 1) Problem: Wyle Coyote was chasing a roadrunner in his acme homemade helicopter. Unfortunately it took him so long to catch up to the roadrunner that he ran out of gas. When he ran out of gas he was...
12. ### Falling Object in Straight Line

An object falling in a vertical line passes a window 3 m high in 1/6 seconds. Find the distance above the top of the window from which the object let fall. No idea about this question at all. I did a=9.8 thus v^2 = 19.8x at v=18 (at end of window) x=16.5 thus origin above window = 13.5...
13. ### Motion equation of a free falling object, with air resistance

I solved it for fun, but a question raised. m \dot v =mg-\gamma v. With the integrating factor method, I reached v=\frac{gm}{\gamma}+e^{-\frac{\gamma t}{m}}C. If I set v(0)=0, I get v=\frac{gm}{\gamma} \left [ 1- e^{-\frac{\gamma t}{m}} \right ]. So when t\to \infty, v\to \frac{gm}{\gamma}...
14. ### falling object

The question: A sphere of mass M(kgs), is fired upward with an initial velocity of 10m/s. It's motion obeys the law dv/dt= -g-(b/a)*v*|v| where v(t)=initial velocity at time t where g=10m/s^2 and b/a=1/10 m^-1 (a)Find the time t1 at which it reaches its maximum height where v(t1)=0 so t1= ...
15. ### Distance of Falling Object

The distance traveled by a falling object (subject only to gravity, with wind resistance ignored) is directly proportional to the square of the time it takes to fall that far. If an object falls 100 feet in 2.5 seconds, how far does it fall in 5 seconds? MY WORK: I developed the equation d...
16. ### Amount of sun falling on a lake

The amount of sunlight falling on each unit of area of a horizontal surface(such as a lake)-which is known as "insolation"- depends on the height of the sun in the sky. It is not unreasonable to suppose that, with t measured in hours from sunrise, d denoting the total hours of daylight, and m...
17. ### At what rate is revenue rising or falling.

Problem: "For the past few months, OHaganBooks.com has seen its weekly sales increase. At the moment OHaganBooks.com is selling 1000 books per week and its sales are rising at a rate of 200 books per week. Also, it is now selling all its book for \$20 each, but the price is dropping at a rate...
18. ### Falling body problem

Given the acceleration function A(t)= 12t^2 + 2 A] Find the Velocity function V(t) with the initial condition when t = 0 then V = 7 B] Find the Distance function S(t) with the initial condition when t = 0 then S = 12 Not sure where to start or if someone could help walk me through this.
19. ### physics with a falling ball

So a ball is dropped from a roof, passing a window 1.2 m tall. It takes 1.25s to pass the said window. It takes 1 more second below the window before it hits the ground. How tall is the building? x=vt+\frac {1} {2}at^2, where v is the starting velocity, x is the distance, t is the time, and a...
20. ### Difference Operator and the falling factorial power of k

I have been able to show by algebraic manipulations that the when one applies the difference operator to "x to the n falling" one finds equality with n times x to the (n-1) falling. I know that I have to use this now, but no matter how I try to manipulate the following expression, I can't get...