Determine the X and Y components of the position vector shown. 2) Find the magni

Question

Determine the X and Y components of the position vector shown. 2) Find the magnitude of the velocity and the magnitude of the acceleration of a particle at time t = 4 s if its position is described by r(t) = cos t i + sin(8t - 4) j m. 3) Determine the unit vectors n1 n0, and n2 for the position vector r = 26i+ 17j + 30k. 4) Determine the work done by the resultant force acting on the block shown as the block slides down the incline from the point A to the point B. Let mg = 100 N, h = 2 m, theta= 45 degree, and mux= 0.2.

Explanation / Answer

(1) X = 0.4cos60 + 0.3cos30

X = 0.46 m

Y = 0.4sin60 - 0.3sin30

Y = 0.2 m

(2)

r(t) = cost i + sin(8t-4)j

v(t) = -sint i + 8cos(8t-4)j

v(4)= -0.07 i + 7.064j

|v| = 7.064 m/s

a(t) = -cost i - 64sin(8t-4) j

a(4) = -0.1 i - 30.046 j

|a| = 30.046 m/s^2

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