1) A vector is given in spherical coordinates by \(\vec{A} = 5t \vec{u_r}\), \(\phi(t) = \frac{t}{2}\), \(\theta(t) = \frac{\pi}{2}\) with t represents the time and. a) Determine the first derivative of the vector \(\frac{d\vec{A}}{dt}\). b) Deduce the cartesian coordinates x(t), y(t), z(t) of vector \(\vec{A}\) at time t.
Added by Edwin H.
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The magnitude of the vector A is given by r = sqrt((5t)^2 + (9t)^2) = sqrt(25t^2 + 81t^2) = sqrt(106t^2) = sqrt(106)*t. Show more…
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