1. The parametric equations of an object are given by x = Rcos(wt), and y-Ksin(ot), where...
F(t) cRsin(wt)â+Rcos(wt)ý, where c, R, w are positive constants Find the angle between the velocity vector and the acceleration vector as a function of time. In particular, what is this angle at a time t T/2w? What does your expression reduce to when c 1? Can you What shape does the particle trace out as it moves through space? explicitly show that the particle's trajectory satisfies the defining equation for this shape?
2. A particle moves in the x-y plane. Its coordinates are given as functions of time t(2 0) b x(t)-R(at-sina)t), )Sketch the trajectory of the particle. This is the trajectory of a point on the rim of a wheel y(t)-R(1-cosω t), where R and ω are constants. (a) (3 that is rolling at a constant speed on a horizontal surface. The curve traced out by such a point as it moves through space is called a cycloid. (b) (5 Find...
The x- and y-coordinates of a moving particle are given by the parametric equations below. Find the magnitude and direction of the velocity for the specific value of t. Sketch the curve and show the velocity and its components. x = 4, y = 4-t,t=2 Find the magnitude of the velocity of the particle for the specific value of t. The magnitude is approximately (Type an integer or decimal rounded to two decimal places as needed.) Find the direction of...
A particle travels along the circular path x2 +y-r, when the time t = 0 the particle it's at-r meter and y =0 m. If the y components of the particle's velocity is Vy 2r cos2t, determine: (a) the x and y components of its acceleration at any instant. (b) Draw the trajectory with the vector velocity and acceleration at t = π/4 sec. (c) calculate the average vector velocity between 0 and t/4 sec. (d) the distance travelled when...
parts a through e please with work. A particle travels along the circular path x2 +y-r, when the time t = 0 the particle it's at-r meter and y =0 m. If the y components of the particle's velocity is Vy 2r cos2t, determine: (a) the x and y components of its acceleration at any instant. (b) Draw the trajectory with the vector velocity and acceleration at t = π/4 sec. (c) calculate the average vector velocity between 0 and...
According to the given equations of motion of the particle M determine the type of trajectory and for a moment of time t=t_1, find its position on the trajectory, its velocity , total tangential and normal acceleration , and a radius of the trajectory curvature. a) X=-2t^2+3,(cm), Y=-5t(cm) , t_1=0.5(s) b) X=-3/(t+2), Y=3t+6, t_1=2
matlab code please 0 solutions submitted (max Unlimited) Problem2 A staircase of height h is modeled by the parametric equations: x = rcos(1) y = rsin(1) -=- trix where r=h[2 + 5 sin(1/8)]/10, n=4, and h 50m is the staircase height. Make a 3-D plot (shown) of the staircase. (Create a vector , for the domain 0 to 2π and use the pi1ot3 command.) so so nd ion Your Script em of 11% iength of vector t is 40e, use,...
6. A package of relief supplies is dropped and moves according to the set of parametric equations given below. Find the velocity and acceleration (magnitude and direction) when t=3.0 s. Draw both vectors on Xy plane. a) x=35t, y=-4.5t2
The coordinates of a bird flying in the xy-plane are given by x(t)=αt and y(t)=3.0m−βt2, where α=2.4m/s and β=1.2m/s2 -sketch the bird path between t=0 and t=2 s. calculate the acceleration and velocity vectors of the bird as functions of time. calculate the magnitude and direction of the bird velocity and acceleration at t=2s. sketch the velocity and acceleration vectors at t=2 at this instant, is the bird's speed increasing, decreasing or not changing? is the bird turning? if so,...
An object is moving around the unit circle with parametric equations x(t)=cos(t), y(t)=sin(t), so it's location at time t is P(t)=(cos(t),sin(t)) . Assume 0 < t < π/2. At a given time t, the tangent line to the unit circle at the position P(t) will determine a right triangle in the first quadrant. (Connect the origin with the y-intercept and x-intercept of the tangent line.) (a) The area of the right triangle is a(t)= . (b) lim t → pi/2−a(t)= ...