A frictionless particle P, starting from rest at time t = 0 at the point (a, 0, 0), slides down the helix r(0) = (a cos 0)i + (a sin 0)j + b0k (a, b > 0)under the influence of gravity, as in the accompanying figure. TheO in this equation is the cylindrical coordinate 0 and the helixis the curve r = a, z = b0, 0 z 0, in cylindrical coordinates. Weassume 0 to be a differentiable function of t for the motion. Thelaw of conservation of energy tells us that the particle's speed afterit has fallen straight down a distance z is V2gz, where g is theconstant acceleration of gravity.a. Find the angular velocity de/ dt when 0 = 2.b. Express the particle's 0- and z-coordinates as functions of t.c. Express the tangential and normal components of the velocitydr/ dt and acceleration d'r/dt² as functions of t. Does theacceleration have any nonzero component in the direction ofthe binormal vector B?The helixr = a, z = b0Positive z-axis

Given: r(θ)=(acosθ)i+(asinθ)j+bθk (a,b>0) {under the influence of gravity}…

Answered: r(0) = (a cos 0)i + (a sin 0)j + b0k…

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