Question

I have the solution to question 1. Need help with 2 and 3.

(1) An object is thrown, and it is subject to the constant acceleration vector i+j-2k. If the position when t=0 is (1,-1,0) and the velocity at t = 0 is i + i + k, when and where does the object fall on the plane z =0? What is the impact velocity? /2 (2) Assume the same context as in Part (1) above, except that we change the initial velocity vector vo. Suppose that we can generate the max speed of 3, i.e., Il voll <3. What should be my initial vector vo at (1,-1,0), so that it lands on the spot (0,2,0)? 1 /2 (3) Assume the same context as in Part (2) above, except that we change the initial velocity vector Vo. What should be my initial vector vo at (1,-1,0), so that it lands on the spot (0,2,0), and voll is as small as possible? /2

Answer 1

given tão, di = î. î , a= êrî - 2ř = axê xayî tq Initial velocity u = îtî tê ay = 1 î m/sech Here 10,90) 4x = 1 7 m/sec My = 1 h my sec 42 = 1 Ê m/sec 9x = 1 ê mera Eqn of motion along z-direction Uz = Uz + azt At maximum Height U2=0 = + = -42 az - sec ine time taken by particle to re ale to reach max height is = sec so particle After Isec reaches at z =0 Hence particle After Li sec Hit the ground → Apply fan of motion in x-y plance → position of particle After t=1sec -o; - ut +za+2 of . (^_ŷ ) = (Q +9) x 1 + + ( ht?). 12 (-). 3, (+9) js = 3+5) + ê- % +47) » (%15,0)

velocity of particle After Isec o= utat u = (hti + ² ) + ( êt? -28). I