What is Kinematics problem: Definition and 281 Discussions
In computer animation and robotics, inverse kinematics is the mathematical process of calculating the variable joint parameters needed to place the end of a kinematic chain, such as a robot manipulator or animation character's skeleton, in a given position and orientation relative to the start of the chain. Given joint parameters, the position and orientation of the chain's end, e.g. the hand of the character or robot, can typically be calculated directly using multiple applications of trigonometric formulas, a process known as forward kinematics. However, the reverse operation is, in general, much more challenging.Inverse kinematics is also used to recover the movements of an object in the world from some other data, such as a film of those movements, or a film of the world as seen by a camera which is itself making those movements. This occurs, for example, where a human actor's filmed movements are to be duplicated by an animated character.
TL;DR Summary: A train on a level stretch of tracks, starting from a dead stop, steadily speeds up to 28 m/s in 2.0 minutes, and then slows to 18 m/s with a constant deceleration of 0.011 m/s^2. What is the average speed of the train for this whole thing (speeding up and slowing down)?
I know...
I tried to write the data I understood from the image:
y0=160m
yf=0
x0=0
x1=192m
I tried to express the total change in time using the position over time equation on the Y direction:
y(t)=y0+v0y*(t2-t1)-0.5a(t2-t1)^2
but then I stuck with 2 variables and didn't know what to do
any help?
So what I have done is that on question 7 I know he is accelerating to constant my knowns are that it is from initial and acceleration is given so I have that for my first phase the second phase is that Your vfinal is your new initial for it and acceleration is the constant but you don't know...
I think Option C should be correct
since the body has two velocities in the same position which is not possible. They even didn't show an arrow that could tell it has which velocity at its starting point and at the ending point
But the given and in my textbook is Option d ( It can have an error...
0=6-4.9(t^2)
0=-27,7t+Xo
From the first equation,
T= 1.10s
From the second equation,
(Xo/27,7)=t
0=6-4.9((Xo/27,7)^2)
We solve for Xo = 30,65
Now, we have
X=-27,7t+30,65
If t=1,10
Then , -27,7(1,10)+30,65=0,18 which is not equal to 0.
Which means the stone hits the ground first.
Is my answer...
Hi folks,
See below for a solved question finding the down slope distance of an arrow. How easy would it be to solve this question by making the x-axis the slope direction?
I've been attempting to solve this problem for three days now. I have thrown away my old attempts (like, scrumpled up into the bin), but my old attempts involved:
Trying to set up simultaeneous equations relating the journeys between EH and FG to find the deceleration, but the reason why this...
Summary: Olympic problem from kinematics
Hello,
could anyone help me with the following problem? I don't quite get how exactly does it work.
After being kicked by a footballer, a ball started to fly straight towards the goal at velocity v = 25m/s making an angle α = arccos 0.8 with the...
So I know that ##a_t = \frac{dv}{dt}=-ks## and ##\frac{dv}{dt}=v\frac{dv}{ds}## then: $$v dv=-ks ds \rightarrow (v(s))^2=-ks^2+c$$ and using my initial conditions it follows that: $$(3.6)^2=c \approx 13$$ and $$(1.8)^2=13-5.4k \rightarrow k=1.8 \rightarrow (v(s))^2=13-1.8s$$
What bothers me is...
A particle, P, starts from rest at a point X and moves in a straight line with an acceleration expressed as a=4t. After 2 seconds, the particle reaches Y and it stops accelerating. The particle leaves Y with a velocity -3ms-1, and finally comes to rest at Z.
(i) Find the value of t when the...
Step 1. Integrate the function --> it comes out to -1.8t3+t2-8t+c
Step 2. Figure out the integration constant --> I know that the velocity of the car is 30m/s at t=0s so making 30m/s = -1.8(0s)3+(0s)2-8(0s)+C it would seem that C is 30m/s
Step 3. Calculate velocity at 4s --> V(4s)=...
Homework Statement
This is a physics problem that I made up in order to understand one aspect of kinematics in 1-dimension: A baseball is thrown straight up, leaving the hand which is 1.1 meter above the ground. It reaches a height of 12 meters. (a) What must be the speed of the baseball when...
Homework Statement
Homework Equations
a=dv/dt, v=dx/dt, x=integ(vdt)
The Attempt at a Solution
We were given the above problem and solution. Everything seems very straightforward. My question is this: should the function for acceleration also include a constant, e.g. [/B]
?
None of the...
Homework Statement
A person throws a ball up from a height of 1.5 meters, 3.23 seconds later, the ball hits the ground next to you. Find the maximum height the ball reaches.
Homework Equations
V=V(initial)+at
The Attempt at a Solution
This problem almost seems impossible without knowing what...
Homework Statement
What minimum time is required to move a weight of mass 50 kg over a distance of 10 meters along a horizontal floor if the rope used to pull it breaks when the tension exceeds 20kgf, while a force of 10kgf is sufficient to start the weight moving or move it uniformly...
Homework Statement
On a North-South highway, a Car drives 80 km/h [N]. A SUV, that is north of the Car, is moving 70 km/h [South]. The car is to the south of the SUV. The two are separated by 20 km. Where are the two cars when they pass each other.
Homework Equations
Both are in uniform...
Homework Statement
Three ants A, B and C are crawling on a large horizontal tabletop always occupying vertices of an equilateral triangle, size of which may vary with time. If at an instant, speeds of A and B are vA and vB, prove that vC>= vA+vB.
Homework Equations
Well, that's what I don't...
1. Problem statement:
"An object is thrown horizontally with an initial speed of 10 m/s. How far will it drop in 4 seconds?"
Homework Equations
Δx = v0x.t
Δy = v0y.t + 1/2(-g)t2
The Attempt at a Solution
[/B]
When I first read it, I thought that 'how far' means Δx, since when someone says...
Homework Statement
A disk is initially at rest. A penny is placed on it at a distance of 1.4 m from the rotation axis. At time t=0s, the disk begins to rotate with a constant angular acceleration of 1.9 rad/s^2 around a fixed, vertical axis through it's center and perpendicular to it's plane...
1. A car accelerates for 200 meters and has an initial velocity of 2.0 m/s and a final velocity of 6 m/s. What is the acceleration of the car if this change in velocity takes 12 seconds?Homework Equations
a=Δv/Δt
Δx=Vi*t+.5at2[/B]The Attempt at a Solution
When I solve this using the first...
Homework Statement
A train 400 m long is moving on a straight track with a speed of 21.6m/s. The engineer applies the brakes at a crossing, and later the last car passes the crossing with a speed of 5.0m/s. Assuming constant acceleration, determine how long the train blocked the crossing...
Homework Statement
Starting from the center of a circular path of radius R, a particle P chases another particle Q that is moving with a uniform speed v on the circular path. The chaser P moves with a constant speed u and always remains collinear with the centre and location of the chased Q...
Homework Statement
A person runs at a constant speed of 4.0 m/s to catch a stationary bus. When she is 6.0m behind it (t=0s), the bus leaves, accelerating with a (constant) acceleration of 1.2 m/s^2. How long does it take her to catch up to the bus?
Homework Equations
X = Xo + Vot + 0.5at^2...
Homework Statement
Because of your technical background, you have been given a job as a student assistant in a university research laboratory that has been investigating possible accident-avoidance systems for oil tankers. Your group is concerned about oil spills in the North Atlantic caused by...
Homework Statement
For each of the following cases, represent on the trajectory, the velocity and tangential and normal components of the acceleration at times t1 and t2 of a mobile that moves according to the graph of s (arc) versus t (time) on the left. The point O on the trajectory marks the...
Homework Statement
Suppose the acceleration of a particle is a function of x, where a(x)=(2.0 s-2)*x.
(a) If the velocity is zero when x= 1.0 m, what is the speed when x=3.0 m?
(b) How long does it take the particle to travel from x=1.0 m to x=3.0 m. a(x)=(2.0 s-2) * x
(a) V(x=3) = ? , V(x=1)...
Homework Statement
Object launched vertically with v initial =20 m/s. No air resistance. How long does it take to reach its max height?
Homework Equations
1/2 at^2 + vot = dy
.5mv^2=mgh
The Attempt at a Solution
I began by using conservation of energy to find the max height. .5mv^2 = mgh...
Homework Statement
The engineer of a passenger train rounding a curve at 30m/s sights a slow-moving freight train 200m ahead on the same track traveling in the same direction with a constant velocity of 10m/s. The engineer of the passenger train immediately applies the brakes, causing a...
Homework Statement
Luke Skywalker is making a diving run at the Death Star, approaching in his X-Wing at a rate of 500m/s. (The Death star is hollow, so it has almost no gravity.) Suddenly, at 800 meters from the Death Star, Luke fires his retro rockets. This creates a reverse acceleration of...
Homework Statement
An Airbus 380 needs to reach the velocity of 280 kmh^-1 before it takes off. The maximum acceleration the plain reaches in the runway is 0.95 ms^-2. Verify THAT the plane can use an airport with this runways.
Runway 1: 3805 meters (SSW-NNE)
Runway 2: 2400 meters (S-N)...
Homework Statement
Horse is running in circle with constant velocity V. In the middle of circle is flashlight, lighting in all directions. Wall is set as a tangent to circle. If horse starts running from tangential point and pass 1/8 of circle, what will be speed of a shadow on the wall? Can...
I'm really lost on this one.
I'm really not sure how to get started on this. I started it out as a force problem and solved for ax = g*cos(theta). I then integrated that (treating it like a constant) from zero to D to find my initial velocity at the time the block reaches the edge of the...
Homework Statement
Q; In an electron gun of television set, an electron with initial speed of 10^3m/s enters a region where it is electrically accelerated. It emerges out of this region after 1micro sec with speed of 4×10^5 m/s.
(a) Find the acceleration.
Homework Equations
vf= vi+at
The...
Homework Statement
A ball starts from rest and rolls down a hill with uniform acceleration, traveling 150 m during the second 5.0 s of its motion. How far did it roll during the first 5.0 s of motion?
Vi= 0
at time t=5s -> d= 150 m
Homework Equations
d=vf+vi/2 * t
The Attempt at a...
Homework Statement
In Example 2.6, we considered a simple model for a rocket launched from the surface of the Earth. A better expression for a rocket's position measured from the center of the Earth is given by
Y(t)=(RE3/2+3(√g/2)REt)2/3
where RE is the radius of the Earth (6.38 ✕ 106 m) and g...
A ball is rolling over a soccer field with constant velocity Vb > 0 at an angle of 45° to the goal line. It starts at the corner of the field (distance d from the middle of the goal line) at the time t0 = 0. At the same time a player starts heading towards the goal on a path perpendicular to the...
Homework Statement
A boat is crossing a river between via points A and B which are d=400m apart. The speed of the river is V2=2 m/s and is constant along the AB line. The angle of the boats trajectory is α=45 degrees. At what speed V2 and with what angle β should the boat be directed so that it...
Homework Statement
Humpty Dumpty had a great fall from a roof. It took him 2.25s to fall. How high was the roof?
Homework EquationsThe Attempt at a Solution
Homework Statement
bicyclist increases its velocity at constant power
a) how great is this power when the bicycle's velocity increases, from 18km/h to 23km/h, during the time of 1,2 seconds
b) Within which boundaries does the acceleration vary? The combined mass of bicyclist and his bicycle...
Homework Statement
http://imgur.com/0t8TVgq
http://imgur.com/0t8TVgq
[Image copy inserted by moderator]
Sorry about all the erase marks. My question is why is the final velocity not 0.
Homework Equations
V=Vo+at[/B]
The Attempt at a Solution
So the question is asking for the horizontal...
Homework Statement
Homework Equations
y = y0 + Vot + 1/2gt²
The Attempt at a Solution
We have to know when yball = y rock
for the ball : t = t-1 because it's throwed 1 sec later the rock.
we have to fine when yball = yrock :
12.t - 0.5*9.8*t² = 18*(t-1) - 0.5*9.81*(t-1)²..I find the answer...
Homework Statement
A ball is rolling towards a rectangular hole which is 40cm deep and 2cm wide with a velocity 1m/s. It falls through the hole, bounces off the walls a couple of times and falls down. The direction of balls motion is perpendicular to the hole (falling in it from one side)...
Homework Statement
A motorist drives along a straight road at a constant speed of 14.4m/s. Just as she passes a parked motorcycle police officer, the officer starts to accelerate at 1.8m/s^2 to overtake her. Assuming the officer maintains this acceleration, determine the time it takes the...
Okay, so. I'm doing a project for an environmental geology course in which I need to create a landslide hazard map. Essentially, I have a mass of rock sliding down an inclined plane. I have calculated the kinetic energy and force of the material as it moves down, as well as the final velocity as...
A rock is dropped from a cliff of height h. At the same time a rock is thrown straight up from the bottom with an initial velocity. Assuming they meet, at what time will they meet.
V1 = 0
A = -9.82
Thats all you have across both rocks... is this even possible. You probably have to do some...
Homework Statement
[/B]
A baseball pitcher throws a ball at a speed of 47m/s. When the catcher receives the ball, he pulls his hand back through a distance of 0.035m in the process of making the catch. What was the acceleration of the ball as it was being caught, assuming the acceleration was...