pls show all ur work Consider an object with a position vector given by What is
ID: 2264460 • Letter: P
Question
pls show all ur work
Consider an object with a position vector given by What is the position of the object at time t = 0. Looking down on the x-y plane, is this object moving counterclockwise or clockwise? Find the velocity of this object. Express your answer using both using Cartesian coordinate unit vectors and in terms of and/or Find the speed of the object. Find the acceleration of this object. Express your answer using both using Cartesian coordinate unit vectors and in terms of and/or Find the magnitude of the acceleration of this object. Problem 3. Consider an object with a position vector given by assume that r and omega are constant and positive. Does this position vector represent motion on a circle? Jusify your answer. Find the speed of the object. Problem 4. A car travelling with a speed of 50 mi/hr barely loses contact with the ground as it drives over the top of a circular hill. Find the radius of the hill. Problem 5. A person of mass 100 kg rides in a Ferris wheel of radius 30 m. The Ferris wheel has a constant rotation rate (omega)Explanation / Answer
a) at t=0 r=0.4*cos(pi/2 )*i +0.4*sin(pi/2)*j =0.4*j m (i is the unitiy vector of x axis, j is the unity vector of y axis)
b) x =r*cos(theta), y=r*sin(theta)
where theta = pi/2-(3/1 s)*t is decreasing from pi/2 to 0 with t increasing. The object is moving clockwise.
c) v = dr/dt = +0.4*(3/s)sin((pi/2-(3/1 s)*t)*i-0.4*(3/s)*cos((pi/2-(3/1 s)*t)*j
in terms of r and theta we have
v = omega x r = d(theta)/dt x r where x is the vectorial prodct and
|omega|= d(theta)/dt =+(3/1 s) (in module)
d) v = |omega|*|r| =(3/1 s)*0.4 =1.2 m/s
e) in Cartesian coodinates
a = dv/dt = -0.4*(3/s)^2*cos((pi/2 -3/1 s)*t)*i -0.4*(3/s)^2*sin(...)*j
In polar coordinates
a = omega x v = omega x (omega x r) here x is the vectorial product
|a| =-|omega|*|v| = -omega^2*|r|
f) |a| =(3/1 s)^2*0.4 =9*0.4 (m/s^2)=3.6 m/s^2
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.