pls let me know how to do this

12. [-/1 Points] DETAILS LARCALC11 12.2.069. A particle moves in the xy-plane along the curve represented by the vector-valued function r(t) = (t - sin(t) )i + (1 - cos(t) )j. (a) Use a graphing utility to graph r. ON4 ON X X O 10 20 30 40 OO 10 20 30 40 ONd X X O O 10 20 30 40 O 0 10 20 30 40 Describe the curve. O cycloid O hyperbola O parabola O circle (b) Find the minimum and maximum values of | |r'| | and | |r"ll. IIt'll | |r'll minimum maximum1. [11 Points] DETAILS LARCALC11 12.3.004. E The position vector r describes the path of an object moving in the xy-plane. Position Vector Point r(t) = ti + (t2 + 8)j (1, 7) (a) Find the velocity vector v(t), speed s(t), and acceleration vector a(t) of the object. v(t) = 5(t) = W a(t) = (b) Evaluate the velocity vector and acceleration vector of the object at the given point. v(1) = EU 3(1) = (c) Sketch a graph of the path, and sketch the velocity and acceleration vectors at the given point. 2. [-/1 Points] | DETAILS l LARCALC1112.3.014. The position vector r describes the path of an object moving in space. Position Vector Time r(t)=3ti+tj+%t2k t=2 (a) Find the velocity vector v(t), speed s(t), and acceleration vector a(t) of the object. v(t) = 5(t) = a(t) = (b) Evaluate the velocity vector and acceleration vector of the object at the given value oft. v(2) = 3(2) = Need Help? 3. [-/1 Points] DETAILS LARCALC11 12.3.026. Use the given acceleration function and initial conditions to find the velocity vector v(t), and position vector r(t). Then find the position at time t = 5. a(t) = efi 4k v(0) = 2i + 7j + k, r(0) = o v(t) = r(t) = r(5) = 4. [/1 Points] LARCALC11 12.3.029. ASK YOUR TEACHER A baseball, hit 3 feet above the ground, leaves the bat at an angle of 45" and is caught by an outelder 3 feet above the ground and 300 feet from home plate. What is the initial speed of the ball, and how high does it rise? (Round your answers to two decimal places.) initial speed ft/s maximum height ft Need Help? Use the model for projectile motion, assuming there is no air resistance and g : 32 feet per second per second. 5. [I1 Points] LARCALC11 12.3.035. ASK YOUR TEACHER A bale ejector consists of two variablespeed belts at the end of a baler. Its purpose is to toss bales into a trailing wagon. In loading the back of a wagon, a bale must be thrown to a position 8 feet above and 16 feet behind the ejector. Use the model for projectile motion, assuming there is no air resistance and g = 32 feet per second per second. (a) Find the minimum initial speed of the bale, v, and the corresponding angle, 9, at which it must be ejected from the baler. (Round your answers to two decimal places.) v = ft/sec 9 = (b) The ejector has a fixed angle of 45. Find the initial speed, v, required. v = ft/sec Need Help