2 OO etisalat 4G 231 PM HW 34 Physics Su E Wiley PLUS Chapte

2% OO etisalat 4G 2:31 PM HW 3&4 Physics Su E Wiley PLUS Chapter 04, Problem 011 The position 7 of a particle moving in an xy plane is given by 7-anon zooni 400-10 7 with 7 n meters and t in seconds. In unit-vector notation, calculate (a) (b) v and (c) for t 2.00 s. (d) What is the angle between the positive direction of the x axis and a line tangent to the particle\'s path 2.00 s? Give your answer in the range of (-1800; 180°). att Number Bv accessing this Qweston Assistanor,you waleamwhae earn points based the Point Potential set by your

Solution

a) given that r = (2t^3 -7t)i + (4-t^4)j

at t = 2 sec

r = ((2*2^3)- (7*2)) i + (4-2^4) j

r = 2i - 14 j

b) v = dr/dt = (6t^2-7)i + (0-4t^3)j

at t = 2 sec

v = (6*2^2 - 7) i - 4*2^3 j

v = 17i - 32j

c) a = dv/dt = 12t i - 12t^2 j

at t = 2 sec

a = (12*2)i -(12*2^2) j

a = 24i - 48 j

d) angle is theta

let a bar = i hat

and b bar = 2i - 14 j

cos(theta) = a bar .b bar / (magnitude of a * magnitude of b )

cos(theta) = 2/(sqrt(1)*sqrt(2^2+14^2)) = 0.141

theta = cos^(-1)(0.141) = 81.9 degrees