Problem 1. Find the lengths of the curves (a) r(t) = for 0 g t g g. (b) Find the curvature of r(t) = (t, t2, (3) at (1,1,1). Problem 4. For this problem, vectors are in the xy-plane, so z = 0. A projectile is fired with muzzle speed 150 m/s and angle of elevation 45 from a position 10 m above ground level. (a) Denote by r(t) the trajectory of the projectile, by v(t) its velocity, and by a(t) its acceleration. Then a(t) = (0, -9.8,0) for all t and r(0) = (0, 10, 0). What is the value of v(0)? (b) Where does the projectile hit the ground (that is, when is y(t) = 0), and with what speed