Physics 231 non calculus introductory physics I Section 003 http www pa msu edu people yuan classes htm http www pa msu edu people yuan classes htm Honors option Serve two hours a week in the helproom BPS 1248 must score 3 5 and above in all midterms PHY 231 PHYSICS 231 Lecture 4 Vectors PHY 231 2 Jumping fish A B C D A fish jumps out of the water with v 5 0 m s straight up At which point is its acceleration 0 m s 2 consider id only l th the ti time after ft jjustt lleaving i the water until just before reentering On its way up On its way down At the highest point Never There is always acceleration due to gravity 9 8 m s2 Know how to solve quadratic equations PHY 231 3 important stuff x t x0 v0t 0 5at t 0 5at2 v t v0 at free fall y t y 0 v0t 0 5gt2 v t v0 gt g 9 8 m s2 on earth g 9 8 PHY 231 4 Vectors and Scalars Scalar A quantity specified by its magnitude only Vector A q quantity y specified p both by y its magnitude g and direction To distinguish a vector from a scalar quantity it is usually written with an arrow above it or in bold to di ti distinguish i h it f from a scalar l Scalar A Vector A or A PHY 231 5 Question Are these two vectors the same Are the lengths of these two vectors the same Two vectors are equal q if f both their length g and direction are the same PHY 231 6 Vector addition A B B A B A B A B B A A PHY 231 7 Vector subtraction B B B A A B A B A B A B PHY 231 8 Vector operations in equations X X X X Xb a b a b a Ya b Ya Yb Ya Yb y xb yb B X a b X a X b X a X b Y Y Y Y Y b a b a b a a b ya b x A B A xa ya x Example X a b 5 3 2 Ya b 2 2 4 PHY 231 9 The length of a vector and its components Y xa ya x Length of vector use pythagorean theorem l x a l cos x a2 y a2 y a l sin tan y a x a PHY 231 10 vector addition PHY 231 11 Question A man walks 5 km h He travels 12 minutes to the east 30 minutes to the south east and 36 minutes to the north A What is the displacement of the man B What is the total distance he walked A X 1 2 3 X 1 X 2 X 3 1 1 77 0 2 77 Y 1 2 3 Y Y Y 2 3 1 0 1 77 3 1 23 displacement 2 77 2 1 23 2 3 03 3 km k 1 km B 1 2 5 3 6 5 km 315o 2 5 km Y2 2 5sin 1 77 x2 2 5cos 1 77PHY 231 12 Another view A X 1 2 3 X 1 X 2 X 3 1 1 77 0 2 77 Y1 2 3 Y1 Y2 Y3 0 1 77 3 1 23 displacement 2 77 2 1 23 2 3 03 3 km 360o 45o 315o 1 km 315o 2 5 km x2 2 5cos 1 77 Y2 2 5sin 1 77 PHY 231 13 Relative motion Motion is relative to a frame A woman in a train moving 50 m s throws a ball straight up with a velocity of 5 m s A second person watches the train pass by and sees the woman through a window What is the motion of the ball seen from the point of view from the man outside the train Motion of the ball in rest frame rest frame of train Resulting motion Motion of the train PHY 231 14 Boat crossing the river PHY 231 15 Question A boat is trying to cross a 1 km wide river in the shortest way straight across Its maximum speed in still water is 10 km h The river is flowing with 5 km h km h 1 At what angle does the captain have to steer the boat the go straight across A 30o B 45o C 0o D 45o 2 how long does it take for the boat t cross to ss th the river i A 6 min B 6 9 min C 12 min D 1 h 3 If it doesn t matter at what point th b the boatt reaches h the th other th side id at what angle should the captain steer to cross in the fastest way A 30o B 45o C 0o D 45 45o PHY 231 16 Answer Counter balance flow 5km h Maximum v 10 km h adjacent Fl Flow 5km h 5k h Opp Opp 1 sin opposite hypothenuse 5 10 0 5 sin 10 5 30o 2 tan opposite adjacent tan30o 0 577 5 velocity 0 577 5 velocityhor velocityhor 8 66 km h time 1 km 8 66 km h 0 115 h 0 115 h 6 9 6 9 min p 3 0o the horizontal component of the velocity is then maximum PHY 231 17 plane in the wind PHY 231 18
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