The position vector r describes the path of an object moving in space. Find the velocity v(t), speed s(t), and acceleration a(t), of the object. r(t) = (3t, 4 cos(t), 4 sin(t)) V(t) = s(t) = a(t)The graph of the vector-valued function r(t) and a tangent vector to the graph at & = to are given. r(t) = (t, -+2, 1+3), to = 1 PA -2, (1, -1. 4) 2 (a) Find a set of parametric equations for the tangent line to the graph at t = to. (Enter your answers as a comma-separated list.) (b) Use the equations for the line to approximate r(to + 0.1). r(1 + 0.1) =Use the model for projectile motion, assuming there is no air resistance. Find the vector-valued function for the path of a projectile launched at a height of 10 feet above the ground with an initial velocity of 72 feet per second and at an angle of 30 above the horizontal. r(t) - Use a graphing utility to graph the path of the projectile. r(t) r(t) O 50 100 150 200 250 300 O 50 100 150 200 250 300 r(t) rit) O 50 100 150 200 250 300 O 50 100 150 200 250 300Use the model for projectile motion, assuming there is no air resistance. Determine the maximum height and range of a projectile fired at a height of 4 feet above the ground with an initial velocity of 700 feet per second and at an angle of 450 above the horizontal. (Round your answers to three decimal places.) maximum height ft maximum range ft