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A particle moves so that its position vector is given by r -coswt i+sin wt j...
A particle moves in the plane with position given by the vector valued function r(t)=cos^3(t)i+sin^3(t)j MA330 Homework #2 particle moves in the plane with position given by the vector-valued function The curve it generates is called an astrid and is plotted for you below. (a) Find the position att x/4 by evaluating r(x/4). Then draw this vector on the graph (b) Find the velocity vector vt)-r)-.Be sure to apply the power and (e) Find the velocity at t /4 by...
A particle moves in an elliptical orbit given by ?⃗=?cos???̂+?sin?? ?̂ where ? and ? are positive constants with ? < ?. Find the speed and acceleration of the particle as a function of time. At what time or times will the acceleration be perpendicular to the velocity? 4. A particle moves in an elliptical orbit given by * = b cos wt î+ c sin wt where b and c are positive constants with c < b. Find the...
Suppose that the position vector of a particle is given by the following function of time: r = (6.0 + 2.0t^2)i + (3.0 - 2.0t + 3.0t^2)j where distance is measured in meters and time in seconds. (a) What is the instantaneous velocity vector at t=2.0 s? What is the magnitude of this vector? (b) What is the instantaneous acceleration vector? What are the magnitude and direction of this vector?
4. A particle moves along the curve y = A12 so that its position is given by x = Bt. (a) Find the position vector of the particle in the form 式t) = x(t) + y(t) j (b) Calculate the speed u = of the particle along this path at an arbitrary instant t.
A particle moves and its vector is given by ? = ??? + (? − ??)? find (a) a unit vector normal to the trajectory at t =1 (b) The angular momentum ? = ? × ??̇ of the particle where ?̇ = ?r/?t (c) The torque ? = ? × ??̈ on the particle where ?̈= ???/??2 Note: from (b) and (c) it is easily seen that ? = ?l/?t Please show all workings out and thanks for your...
A force acting on a particle in the xy plane at coordinates (x, y) is given by vector F = (F_0/r) (y hat i - x hat j), where F_0 is a positive constant and r is the distance of the particle from the origin. Show that the magnitude of this force is F_0. Show that the direction of vector F is perpendicular to vector r = x hat i + y hat j.
The vector r(t) is the position vector of a particle at time t. Find the angle between the velocity and the acceleration vectors at time t = 0. r(t) = sin (3t) i + In(31 2 + 1)j + V32.1k os Oo 4 Moving to the next question prevents changes to this answer.
A rabbit runs in a parking lot such that its position vector is given by the function, which is defined as r(t) (3t^2+7) i + (2t-5) j, where r is in meters and t is in seconds. Find the magnitude and direction of the acceleration of the rabbit at t= 1 s
The vector position of a particle varies in time according to the expression r-7.40 i-8.20t2 j where r is in meters and t is in seconds. (a) Find an expression for the velocity of the particle as a function of time. (Use any variable or symbol stated above as necessary.) m/s (b) Determine the acceleration of the particle as a function of time. (Use any variable or symbol stated above as necessary.) m/s2 (c) Calculate the particle's position and velocity...
The position vector of a point which moves in the x-y plane is given by: r = (- 0.2 t4 + 1.8 t3 + 1.1 t2) i + (- 0.4 t4 - 1.2 t) j where r is in meters and t is in seconds. Determine the angle between the velocity v and the acceleration a when t = 1.7 sec.