Determine whether the following trajectory lies on either a circle in R2 or a sphere in R3 centered at the origin. Ifso. nd the radius of the circle or sphere. and show that the position vector and the velocity vector are everywhere orthogonal. rIIt]I= [:11 cos 2t.11 sin 2t). for t] SISI Determine whether the following trajectory lies on either a circle in R2 or a sphere in R3 centered at the origin. Select the correct choice below and. if necessary. ll in the answer box to complete your choice. [:1 A. The trajectory lies on a circle with radius . [Simplify your answer.) [:1 E- The trajectory lies on a sphere with radius .{Simpliiyr your answer] [:1 C. The trajectory does not lie on a circle or a sphere. Given an acceleration vector, initial velocity (Up.Vo), and initial position (x0,yo), find the velocity and position vectors for t20. a(t) = (0,1) , (Up,Vo) = (6,6), (xo yo) = (0,0) What is the velocity vector? v(t) =Consider the motion ofa soccer ball that is kicked from the point {Xe-Yo} = {0.0} with an initial velocitg.r of {u0,vu> = {25.3'} mis. Assume the xaxis is horizontal: the positive vaxis is vertical [opposite g}. the ground is horizontal. and only the gravitational force acts on the object. a. Find the velocitv and position vectors for t2 [1. b. lGraph the trajectory. c. Determine the time of flight and range of the soccer ball. d. Determine the maximum height of the soccer ball. a. The velocity vector is vit] = ED. Given an acceleration vector, initial velocity (Up.Vo,wo), and initial position (X0.yoZo), find the velocity and position vectors for t2 0. a(t) = (t. e -9), (up, vo.wo) = (0,0,2). (xo. yozo) = (6,0,0) What is the velocity vector? v(t) =Consider the motion of a bullet that is fired from a rifle 1 m above the ground in a northeast direction. The initial velocity of the bullet is (100,100,0) . Assume the x-axis points east, the y-axis points north, the positive z-axis is vertical (opposite g), the ground is horizontal, and only the gravitational force acts on the object. a. Find the velocity and position vectors for t2 0. b. Make a sketch of the trajectory. c. Determine the time of flight and range of the bullet. d. Determine the maximum height of the bullet. a. The velocity vector is v(1) = (Simplify your answers. Use integers or decimals for any numbers in the expressions.)A projectile is fired over horizontal ground from the origin with an initial speed of 70 m/s. What firing angles will produce a range of 400 m? Angles of degrees will produce of range of 400 m. (Do not round until the final answer. Then round to two decimal places as needed. Use a comma to separate answers as needed.)