A particle P travels along an elliptiral spiral path such that ts poston ector r

Question

A particle P travels along an elliptiral spiral path such that ts poston ector ris dehned by r={2cos(0.1tji + 1.5 in(0.1tjj + (2t)k) m where tisn seconds and the arguments tor the sine and cosine are given in adians Figure 1) Part When t 8 s determine the coordinate direction angles and which the binormal axis to the osculating plane makes with the ar, velocity vr and acceleration ap of the partice in terms of their jk components. The binormal is parallel to VP x ar. Express your answers using three significant figures separated by commas. and z axes. Hint Solve for the , ,- degrees Submit gure 1 of 1

Explanation / Answer

r = 2 cos(0.1t) i + 1.5 sin(0.1t)j + 2t k

at t = 8 sec ,

r = 1.39 i + 1.076 j + 16 k

|r| = sqrt(1.39^2 + 1.076^2 + 16^2)

= 16.1

alpha = cos^-1(1.39 / 16.1) = 85.0 deg

beta = cos^1(1.076 / 16.1) = 86.2 deg

gamma = cos^-1(16/16.1) = 6.39 deg

Ans: 85.0 , 86.2 , 6.39

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