Can you answer question 2 please zoOM+ Evaluate the definite integral tet), 8t 12, 12 d...

zoOM+ Evaluate the definite integral tet), 8t 12, 12 d (Hint: remember integration by parts?) 2. Acceleration due to gravity near the surface of the earth is roughly 32 ft/s. If a particle moving near the ground has no other sources of acceleration. can represent its accelera the (constant) vector function tion (0,0,-32) Imagine a peso sanding on flat ground firing a rifle parallel to the ground. Let p the bllet's veloc- n of the 0 to be the moment that the bullet exits the rifle. Furthermore, let ity. Fix P0)(0,0,5) and 0)(1500, 2000, 0) resistance and any forces other than gravity which would affect the acceleration Neglect of the bullet (a) In this scenario the ry-plane represents the flat ground. From what height (in feet) above e ground is the bullet fired? What is the initial speed of the bullet? (Hint: if you simplify the initial speed calculation it comes out to be a "nice" number) (b) Find t), the path of the bullet. In other words, solve the differential cquation (0,0,-32) for the given initial conditions (c) The bullet flies without hitting anything until it strikes the ground (ry-plane). How long does it ake the bullet to hit the ground? what point does the bullet land? (d) What is the approximate horizontal distance travelled by the bullet before it strikes the e tip of the rifle sits ahove the origin, what is the distance from ground? That is, since the origin to the point where hullet lands?