Aitnt Pofeo: Zhou Yufeng N3.-0-5, 6790-448, yfzhou@ntu.edu.g http://www3.ntu.edu.g/home/yfzhou/coue.html
. A pojectile i fied t flling tget hown. The pojectile lee the gun t the me intnt tht the tget dopped fom et. Auming tht the gun i initilly imed t the tget, how tht the pojectile will hit the tget. (One etiction i tht the pojectile mut ech the tget befoe the tget tike the floo. Set up efeence fme, the initil condition of two pticle ( fo the pojectile, fo the tget e (x (0, y (0=(0,0, nd (x (0, y (0 = (L, L tn y ( 0 0 in, x (0 0 co, y (0 0 whee i contnt. We e ked to poe tht when x = L, y = y
(i The motion of the pojectile cn be expeed co t ( y ( t in t gt x ( t 0 (ii The motion of the tget cn be expeed 0 ( x ( t L (3 (iii when x = L, fom ( we he y( t gt L tn (4 t* L 0 co (5 Subtituting (5 into ( nd (4 yield y ( t* L tn gt * y( t* L tn gt * Poed!
. At gien intnt the jet plne h peed of 0 nd n cceletion of cting in the diection hown. Detemine the te of incee in the plne peed nd the diu of cutue of the pth. Set up the efeence fme, nd expe the gien ecto 060(, ˆ i 0 ( So we cn he the tngentil cceletion t co 60 eˆ t 0.560( which i the tio of the chnge of peed. And the noml cceletion i n Since co 30 n eˆ n, we he 0 79( m 8.9 n 8.9 30(
3. A motoit i teling on cued potion of high wy of diu 350 m t peed of 7 kh. The bke e uddenly pplied, cuing the peed to decee t contnt te of.5. Detemine the mgnitude of the totl cceletion of the utomobile ( immeditely fte the bke he been pplied, (b 4 lte. Show the pth coodinte, nd expe the gien cl 0 7( k h 0(, t.5(, 350( m ( When t = 0 n 0.49( m / 350 0 (b When t = 4 0 tt 0.54 5( n t n.694( 5 0.6486( m / 350 0 t n.406(
4. The ottion of od OA bout O i defined by the eltion t, whee i expeed in din nd t in econd. Coll B lide long the od in uch wy tht it ditnce fom O i, whee i expeed in millimete. When t =, detemine ( the elocity of the coll, (b the totl cceletion of the coll, (c the cceletion of the coll eltie to the od. (i the motion of the od to be t, 4t, 4 (ii the motion of coll eltie to the od to be 3 60t 0t, 0t 60t, 0 0t So, t t =, we he 3 60t 0t, 4, 4 40, 60, 0 ˆ e coiˆ inˆj 0.46ˆ i 0.9093ˆj eˆ co( ˆ i in( ˆj 0.9093ˆ i 0.46ˆj
( the elocity of the coll i the elocity combintion B B f ( / B' the eltie elocity of B eltie to the od (f e ˆ 60ˆ e 4.97ˆ i B/ f 54.56 ˆj ( the entined elocity of B B ' eˆ (40 4ˆ e 45.49ˆ i 66.58 ˆj (3 Combining ( nd (3 gie B 70.46ˆ i.0 ˆj 70.984.03( m (4
(b the totl cceletion of the coll i the cceletion combintion C B B/ f B' B (5 the eltie cceletion of B eltie to the od (f eˆ B / f 0 (6 the entined cceletion of B i B' eˆ eˆ 60ˆ e 640eˆ (7 the Coiolo cceletion C kˆ 8kˆ (60ˆ e B B/ f B/ f 480eˆ (8 Combining (6 nd (7 nd (8 gie B 640ˆ e 640ˆ e 640( 0.493ˆ i.354 ˆ j 905.0849.6( m (9
5. A ocket i fied eticlly fom lunching pd t B. It flight i tcked by d fom point A. Detemine ( the elocity of the ocket in tem of b, nd, (b the cceletion of the ocket in tem of b,,, nd. Setup the efeence fme, decibe the poition of P by P(x P, y P x P b con tn t x P 0, x P 0 y P b tn Uing the definition of elocity gie d y ( btn bec P dt Uing the definition of cceletion gie d y P dt b(ec d ( b tn dt b(ec b ec tn
6. The pin t B i fee to lide long the cicul lot DE nd long the otting od OC. Auming tht the od OC otte t contnt te, ( detemine the cceletion of pin B, (b detemine the eltie liding elocity nd cceletion of the pin eltie to the otting od OC. Setup two fixed efeence fme O-xy, A-x y, fo the ngul poition of B, we he =. Theefoe. Since i contnt, we cn he contnt nd 0 ( Meuing the motion of B in A-x y : b e ˆ b eˆ b eˆ B theefoe B b eˆ B b ' c ( b ( ( b ( (4b ( which i pointing to point A.
(b Obeed fom the fme (f fixed on od OC, the eltie motion of B i decibed by e, eˆ ˆ B/ f B/ f Expeing in tem of by bco we cn deie bin bin bco Hence B/ f bin e B/ f bin bco e whee e co i in j