The second part this question is The direction is approximately_____? Document1-
ID: 2868631 • Letter: T
Question
The second part this question is
The direction is approximately_____?
Document1-Word http /Www.matl I:COm 24.3.3 Ex. Score: 3 of 9 pts HW Score: 53.5% (53.5 of 100 pts) 11 of 11 complete 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. 90 AV x=3t, y-2-t,t24 Find the magnitude of the velocity of the particle for the specific value of t. The magnitude is approximately More (Type an integer or decimal (Type an integer or decimal rounded to two decimal places as needed.) Enter your answer in the answer box, then click Check Answer Clear All Check Answer Save 2:53 PM 4/25/2015Explanation / Answer
given parametric equations are x= 3t, y= 2-t. They give the position of a particle at any time t.
To find the velocity, differentiate x and y with t, then we get x and y component of velocity respectively.
So x component of velocity = dx/dt =d/dt(3t) =3 ad
y component of velocity = d/dt(2-t) = -1.
In vector form velocity of object is given by 3i -j and magnitude of velocity is (3^2+1^2)^1/2 = (10)^1/2. Note that here velocity is independent of time and at any time, velocity is same at t = 4, velocity will be3i -j and magnitude is (10)^1/2
direction is given by tan-1(vy/vx) = tan-1 (-1/3) = 0.321 radians or -18.418 degree from positive x axis.