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The vector function r(t) is the position of a particle in space at time t. Determine the graph of the position function. r(t) =(t cost)i + (t sin t)j + 2tk Choose the correct graph below. O A. OB. OC. OD.Solve the following initial value problem for r as a function of t. Differential equation: = 2eti-e - tj+ 8e 2tk dt 2 Initial conditions: r(0) =5i + 5j + 5k dr dt = -2i + 6j It = 0 r(t) = + it kAt time t =0, a particle is located at the point (7,7,9). It travels in a straight line to the point (5,5,2), has speed 6 at (7,7,9) and constant acceleration -2i-2j -7k. Find an equation for the position vector r(t) of the particle at time t. The equation for the position vector r(t) of the particle at time t is r(t) = i + + K. (Type exact answers, using radicals as needed.)An athlete puts a 16-lb shot at an angle of 60" to the horizontal from 6.5 ft above the ground at an initial speed of 44 ft/sec. How long after launch and how far from the athlete does the shot land? The shot remains in the air for seconds. (Round to two decimal places as needed.)