Problem 4. For this problem7 vectors are in the xy-plane, so 2 = 0. A projectile is red with muzzle speed 150 m/s and angle of elevation 450 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? Problem 5. Let r(t) be a curve with unit speed. Are the velocity V(t) = r\"(t) and acceleration a(t) : r\"(t) perpendicular for all values 15? Motivate your answeri if yes: explain why this is the case; if no, provide an example where this does not happen. Problem 7. True of False? Please motivate your answers. (a) Assume a particle has trajectory r(t)7 velocity v(t), and acceleration .303). Then d E (b) Assume r1(t) and r2(t) are two vector functions with the same space curve. Assume r1(0) : r2(0). Then the tangent vectors rim) and r'2 (0) are equal (r(t) >