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.
I'm stuck doing this problem in my first year mechanics class. I feel sort of dumb for not being able to get it. The teacher wants us to just memorize the formulas but I really really really don't want to do that - I'm trying to just do it using the basics and calculus. I can obviously do this...
Homework Statement
A pilot flies horizontally at 1300 km/hr at height 35m above initially level ground. At t= 0 the pilot begins to fly over ground sloping upward at an angle of 4.3 degrees. If the pilot does not change his heading, at what time will he hit the ground?
Homework Equations...
Homework Statement
A stone thrown horizontally from a height of 6.02m hits the ground at a distance of 13.90m. Calculate the initial speed of the stone. Neglect air resistance.
Homework Equations
1. v = v0 + at
2. x = x0 + (1/2)(v0+v)t
3. x = x0 + v0t + (1/2)at^2
4. v^2 = v0^2 +...
Hi, I've been stuck on this problem for a bit and I am not really sure how to go about solving it.
Homework Statement
As a traffic light turns green, a waiting car starts with a constant acceleration of 6.0 m/s². At the instant the car begins to accelerate, a truck with a constant...
Homework Statement
An autographed baseball rolls off of a 1.2 m high desk and strikes the floor 0.41 m away from the desk. The acceleration of gravity is 9.81 m/s2 . How fast was it rolling on the desk before it fell off?
Answer in units of m/s.
Homework Equations
You might need to...
Homework Statement
To protect his food from hungry bears, a boy scout rasies his food pack with a rope that is thrown over a tree limb at height h above his hands. He walks away from the vertical rope with constant velocity (v boy), holding the free end of the rope in his hands.
(a) Show that...
Homework Statement
You drive on Interstate 10 from San Antonio to Houston, half the time at 67 km/h and the other half at 112 km/h. On the way back you travel half the distance at 67 km/h and the other half at 112 km/h. What is your average speed (a) from San Antonio to Houston, (b) from...
at an instant two particles, A and B are separated by 'l' distance. A particle is going north with a uniform velocity of u. and the speed of B is v. initially the velocity vectors are perpendicular. always velocity of B is aimed towards A . find when they converge.(meet)
(v>u)
Homework...
Homework Statement
A 12 metrick ton train is moving with a 72KMH velocity.when brakes It comes to rest in 2 mins.find the force caused by the force?
Homework Equations
F=ma
a=v/t
The Attempt at a Solution
didn't get the correct answer which is given on the answers page(only the...
Hello :)
I'm self-studying for my Edexcel Mechanics 2 GCE A Level exam (it's in 10 days :S) and was having lots of trouble with one of the kinematics questions. I've uploaded photos of the problem and my solution for part (a) of the question. I couldn't use the math notation feature on the...
Homework Statement
A tennis player hit the ball giving it velocity v0(speed) whose direction is horizontal. Neglecting the air velocity.Are given (in meters) :
height of player:2,40m
Distance from player to the net of the tennis court:15m
Height of the net:0,9m
What is the smallest value...
Homework Statement
Will a ball, kicked at 14.0 m/s vertically and 9.0 m/s horizontally, clear a bar 3.0 m high and 20 m away from the kicker? Solve.
Homework Equations
Kinematics Equations.
The Attempt at a Solution
Haven't encountered this type of problem, didn't know where to...
Homework Statement
An object is dropped from a tower. if it had been thrown down at 60m/s, it would have taken half the time. What is the height of the tower? (Use gravity as 10m/s2)
Givens
Acceleration = 10m/s2
v1 = 0m/s (not sure)
v2 = 60m/s
time = t/2
Homework Equations...
Homework Statement
A train pulls away from a station with constant acceleration of .4 m/s^2. A passenger arrives at a point next to the track 6.0s after the end of the train has passed the very same point. What is the slowest constant speed at which she can run and still catch the train...
Homework Statement
The motion of a human body through space can be modeled as the motion of a particle at the body's center of mass. The components of the position of an athlete's center of mass from the beginning to the end of a certain jump are described by the following two equations...
Homework Statement
What if the acceleration is not constant? A particle starts from the origin with velocity 8 i m/s at t = 0 and moves in the xy plane with a varying acceleration given by vector a = (7√t j) m/s2, where t is in s. Answer the following using t as t as necessary.
Determine...
Homework Statement
A 95-kg box is sliding along a level floor with a vi of 15m/s.
a) how large of a constant frictional force is needed to stop to box in a distance of 15m?
b)What is the coefficent of friction between the box and the floor.
Homework Equations
I tried to use...
Homework Statement
3. A cannon ball is launched from a cliff with an initial velocity of 50 m/s 300 above the horizontal. If it’s range is 300 m.
a)What is the height of the cliff?
b) What is the impact velocity of the ball right before it strikes the ground?
Homework Equations...
Homework Statement
A bolt comes loose from underneath an elevator that is moving upward at a speed of 7.1 m/s. The bolt reaches the bottom of the elevator shaft in 3.6 s.
(a) How high up was the elevator when the bolt came loose?
(b) What is the speed of the bolt when it hits the bottom...
Homework Statement
A hollow cylinder of length L and radius R has a weight W. Two cords are wrapped in the same direction around the cylinder, one near each end. The cords are fixed to the ceiling. The cylinder is held horizontally with the cords vertical. The cylinder is then released. Find...
Homework Statement
A cannonball is fired from the ground at an angle of 50 degrees. The ball lands 67 meters from where it was fired. Air resistance is negligible.
How long was the ball in the air?
With what velocity was the cannonball fired?
Homework Equations
Xf=.5at2+Vot+Xo...
Homework Statement
A ball is dropped from rest from a height h above the ground. Another ball is thrown vertically upward from the ground at the instant the first ball is released. Determine the speed of the second ball if the two balls are to meet at a height h/2 above the ground...
Hello my name is Unto
I currently study Physics (it's my first year) at the University of Bristol in England.
I first came here with a really horrible relativistic kinematics problem, but I got no answers and managed to solve it myself.
However you seem like nice guys, and it's always...
Homework Statement
Two cars are at the start lines of two roads at right angles to each other and pointing to the intersection 500 metres away. Car A starts from rest with uniform accelereation of 0.5m/s2 and accelerates for 20 seconds. It then continues at the speed reached. Car B starts 5...
A long jumper leaves the ground at 45o above the horizontal and lands 9.1m away. What is her "takeoff" speed?
Well I have
Dx=VxT, but I'm missing some variables, and substitution is failing me. How can I solve this?
A baseball is through across the plate at 44.1 m/s. If it had been through straight up, how high would it have gone.I'm not sure how to find the displacement since all I'm given is the initial velocity. Am I missing something here?
A basic kinematics problem that I just can't get for some reason. I'm having trouble visualizing the graph.
Homework Statement
What's the average acceleration if a car's going 12 m/s constant speed, then accelerates for 12 seconds at 1.7 m/s^2 acceleration?
Variables: none?
Homework...
A "Different" kind of kinematics problem..
A motorcycle daredevil wants to set a record for jumping over burning school buses. He has hired you to help with the design. He intends to ride off a horizontal platform at 40m/s, cross the burning buses in a pit below him, then land on a ramp sloping...
Homework Statement
The height of a helicopter above the ground is given by h=2.90t^3, where h is in meters and t is in seconds. After 1.80 s, the helicopter releases a small mailbag. Assume the upward direction is positive and the downward direction is negative.
A) what is the velocity of...
I believe the solution to this is probably easy, but for some reason I just can't understand it. Any help would be GREATLY appreciated!
Homework Statement
Consider a point at x2 = h/2. Find the rate of closure of the angle between two material lines in the x1 and x2 directions. Find the rate...
Hi Guys, its my first post here and I have a feeling that I'll be using this forum as a resource. Maybe once I learn enough I'll be able to contribute in solving other peoples' homework problems.
Anyway, to the problem:
Homework Statement
A commuter train travels between two downtown...
Homework Statement
If you step on your car's brakes hard, the wheels stop turning (i.e., the wheels "lock") after 2.0 revolution.
Part A.
At the same constant acceleration, how many revolutions do the wheels make before stopping if your initial speed is twice as high?
Homework...
In reaching her destination, a backpacker walks with an average velocity of 1.31 m/s, due west. This average velocity results because she hikes for 6.44 km with an average velocity of 2.54 m/s, due west, turns around, and hikes with an average velocity of 0.475 m/s, due east. How far east did...
A hot air balloon has just lifted off and is rising at the constant rate of 1.30 m/s. Suddenly, one of the passengers realizes she has left her camera on the ground. A friend picks it up and tosses it straight upward with an initial speed of 9.40 m/s. If the passenger is 2.30 m above her friend...
Homework Statement
A motorist travels at a constant speed of 39.0 m/s through a school zone; exceeding the posted speed limit. A policeman, waits 7.0 s before giving chase at an acceleration of 3.5 m/s2. Find the time required to catch the car, from the instant the car passes the policeman...
Homework Statement
Driving along a crowded freeway, you notice that it takes a time t to go from one mile marker to the next. When you increase your speed by 8.4 mi/h, the time to go one mile decreases by 13 s. What was your original speed? So we know the question is asking for velocity...
Homework Statement
A particle starts from rest at (r0) = 9m j-hat and moves in the xy-plane with the velocity shown in the figure . The particle passes through a wire hoop located at (r1)=20m i-hat, then continues onward...
Homework Statement
You are designing a missile defense system that will shoot down incoming missiles that pass over a perimeter defense post. The set-up is shown below. An incoming missile passes directly above the defense base. Radar at the base can measure the height, h, and speed, v1, of...
Homework Statement
The drive propeller of a ship starts from rest and accelerates at 2.90e-3 rad/s^2 for 2.1e3 seconds. For the nest 1.4e3 seconds, the propeller rotates at a constant angular speed. Then it decelerates at 2.3e-3 rad/s^2 until it slow (without reversing direction) to an...
Homework Statement
A small steel ball, dropped from rest, takes 0.5s to fall through a vertical distance of 1.25m.
Determine the actual speed of the ball when it has fallen through a vertical distance of 1.25m, assuming that acceleration is constant.
Homework Equations
v=s/t
The...
3. A daring cowboy sitting on a tree limb wishes to drop vertically onto a horse galloping under the tree. The speed of the horse is 10. m/s, and the distance from the limb to the saddle is 3.0 m.
a. What must be the horizontal distance between the saddle and the limb when the cowboy makes his...
Homework Statement
You throw an object directly upward at the same time a person drops an object down to you from a height, H. The two objects pass at a height H/2. With what speed did you throw the object upward?
Homework Equations
Simple kinematics equations.
The Attempt at a...
[Resolved] Kinematics problem?
Homework Statement
A small ball rolls horizontally off the edge of a tabletop of height h. It strikes the floor a distance x horizontally away from the edge of the table. (a) How long is the ball in the air? (b) What is its speed at the instant it leaves the...
Homework Statement
A car traveling @ 20 m/s pulls out to pass a truck traveling @ 18m/s. The car accelerates for 2.0m/s^2 for 4s and maintains new velocity.
(c.) If the car was originally 8.0 m behind the truck when it pulled out to pass, how far in front of the truck is the car 10.0 s later...
Homework Statement
A train at constant acceleration is traveling in a straight line. It passes two points at a velocity of 50km/h and 80km/h respectively. What is the exact velocity of the train when it is halfway between these two points?
Let v be the exact velocity of the train when it...
Homework Statement
A satellite is in motion over the Earth. The Earth is modeled as a sphere of radius R that rotates with constant angular velocity "\Omega" in the direction of Ez, where Ez, lies in the direction from the center of the Earth to the North Pole of the Earth at point N. The...
I'd really appreciate help on another kinematics problem. This one is harder than the first.
1. A stone is thrown vertically upward with a speed of 12.0 m/s from the edge of a cliff 70.0 m high (Fig. 2–34). (a) How much later does it reach the bottom of the cliff? (b) What is its speed just...
I have been wrestling with this problem for a few days and it is really frustrating me. The image below shows a bar of length l whose endpoints are constrained to move along the lines shown. Point A moves at a constant velocity to the right and I want to find the angle theta as a function of...
A 2.3 103 kg car starts from rest and accelerates along a horizontal roadway to +17 m/s in 21 s. Assume that air resistance remains constant at -500 N during this time. Find
(a) the average power developed by the engine and
(b) the instantaneous power developed at t = 15 s.
I am...
Beginner's Kinematics Problem
Homework Statement
An x-axis likes along an inclined plane, with the positive x-direction down the plane. Two objects A and B travel along the x-axis.
At t=0, object A starts at x=0 with an initial velocity of 0. At t=1s, object B starts at x=10.00 m with a...