Question

Can you answer question 2 please

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?

Answer 1

. Evaluate the definite intcgral tecest8t 12, 1 d t erets , e-d, azte)dt > Sfmfntt <- -8, 3-%+h > 2 7-e 2 1 (a) In this scenario the y-plane represents the flat ground. From what height (in feet) above the ground is the bullet fired? What is the initial speed of the bullet? F S .mponenk z- Enitsal Speed 2 2 SUTO (b) Find t, the path of the bullet. In other words, solve the differential cquation (0,0,-32) for the given initial conditions. Zusyerfoaur Zet Ces ,32t +C3);wh C, C ACg dt we. are ctanh. At tzo V)=<Isco, 4z/500, Ca= 200 & Ca = O UID, 2000,-32t) (Iotra,124rg we whave a,a2,a2 re novanb. plo=<0,0, 5 a0, ar0 & az-5 Sa,Pt)(ist, 20mt, s-t Art to, (c) The bullet flies without hitting anything until it strikes the ground (r-plane). How long does it Lake the bullet to hit the ground? Al what point does the bullet land? 2 S-6t o 1. s secmds o) S-16 4 (d What is the approximate hoizontal distance travelled by the bullet before it strikes the grounl? That is, since the tip of the rifle sits ahove the origin, what is the distance from the origin to the point where bullet lands? The hoztzotal 5o s) 375 distamce travellee