Practice Midterm #1 Solutions. Physics 6A

Transcription

1 Practice Midter # Solution Phyic 6A

2 . You drie your car at a peed of 4 k/ for hour, then low down to k/ for the next k. How far did you drie, and what wa your aerage peed? We can draw a iple diagra with ditance and tie. For each ection we ue the forula Ditance Speed x Tie Section x k ( k 4 ( Section 4k ( k ( t t 4 k k / The total ditance i 6k. Total tie i 5/. Diide thee to get the aerage peed: 6k ag.peed 6 anwer (b 5 k

3 . A peeding car i traeling at 4 / down a traight road. The drier la on the brake, and the car coe to a coplete top in 5 econd. Auing contant acceleration, how far did the car trael while braking? We can ue one of our kineatic forula. ( x x + a Thi forula will work, but we need to find the acceleration firt. We can ue 4 a 8 + at + ( a( 5 Now plug into our preiou equation: x x + a ( x x ( ( ( x x Anwer (c

4 . A rock i town upward fro the top of a -eter high cliff. The initial peed i /. If we ignore air reitance, how long doe it take for the rock to hit the ground below? Firt we can draw a ketch and chooe a coordinate yte. I hae choen the ground a y. That ake the initial height y. / We alo know the initial elocity, and the final height. We can ue one of our baic kineatic equation: y y t + g t Thi gie u a quadratic equation, which we can ole with the quadratic forula. + ( t 9.8 t b ± b 4ac 4.9 t t t a ± t 4( 4.9( ( 4.9 or t 8.9 ec t 6.9 ec y y Chooe the poitie alue. Anwer (b.

5 4. Two rock are town with the ae initial peed fro the top of a -eter high cliff. Rock A i town upward and Rock B i town downward. If we ignore air reitance, which of the following i true about the peed of the rock jut before they hit the ground? a Rock A i fater. b Rock B i fater. c Rock A and Rock B hae equal peed. d There i not enough inforation to deterine the anwer. The rock will both land at the ae peed. Rock A goe up to oe high point, then turn around. By the tie it pae the tarting point on the way down, it i oing at the initial peed, jut oppoite direction. So it i jut like rock B at thi point. Of coure rock B hit firt, but they are both oing the ae peed when they hit. Anwer (c Rock A y Rock B y y y

6 5. The radiu of Venu i about 6 k. Auing Venu i pherical, what i it approxiate olue? (V 4πR / for a phere of radiu R Thi quetion i all about unit. We are gien R6 k. We can alo conert thi into or c. R 6 k 6 R 6 8 R 6 c Now we can jut plug thee nuber into our equation: V V V 4π 4π 4π Anwer (d ( 6 k 9.5 k NO 6 ( k NO 8 6 ( 6 c 9.5 c YES

7 6. An airplane i flying Eat at a peed of k/. A gut of wind blow in a Northwet direction at 5 k/. Find the new peed and direction of the plane. We need to add the ector together, o firt we ut find their coponent: y plane,x plane,y wind,x wind,y + k ( 5 k co( 45 ( 5 k in( 45 k k k Northwet ean halfway between North and Wet 5 total x Now add the coponent together, x with x and y with y. total,x total,y k k k k k k Finally, we can put thee coponent together uing the Pythagorean Theore: r ( ( 5.4 k total 67 We can calculate the angle fro our right-triangle rule, and look at our picture to ee that the plane i flying a little bit North of Eat. 5.4 tanθ θ Anwer (c

8 7. Bob ha pet rock. Their nae are Eli and Pedro. Bob drop Pedro fro a high bridge to the rier below. When Pedro ha fallen 4, Bob drop Eli. A the rock continue their free-fall, what happen to their eparation ditance? a The ditance increae. b The ditance decreae. c The ditance tay the ae. d There i not enough inforation to deterine the anwer. Think about the peed of the rock. Since Pedro get a head tart, he i already oing when Eli tart to fall. So Pedro i oing fater than Eli, and they both continue to accelerate at the ae rate (graity. Both peed keep increaing, but Pedro i alway fater. Thu Pedro oe farther than Eli during each econd of their fall. So a they fall, the rock get farther apart. Anwer (a

9 8. A ball i dropped fro a train oing on a traight leel track at a peed of 5 /. The ball i initially 5 aboe the ground. If air reitance can be ignored, how far doe the ball trael horizontally before it hit the ground? 5 / Firt, draw a picture. Thi i a projectile proble, o we ue x x + x,x a x,x t y y +,yt gt,y gt, y g ( y y We are gien the initial peed (horizontal launch, and the initial height. Notice that to find the horizontal ditance, we will need to find the tie it take for the ball to hit the ground. We need to ue the firt ertical equation: y y t + gt t t. Now put thi tie into the x equation: x x x + + Anwer (c,x t ( 5 ( X?

10 9. A occer ball i kicked at an angle of aboe the horizontal on a leel field. The ball land 45 fro where it wa kicked. What wa the initial peed of the ball? Again, tart with a picture. The initial elocity will break down into coponent a follow: coθ,x,y inθ Thi i a projectile proble, o we ue our projectile forula: x x +,xt y y +,yt gt x,x,y gt ax, y g( y y oy θ ox 45 Siilar to the preiou proble, we can find the tie fro the y equation, then plug into the x-equation. y y + gt t + ( inθ,y ( inθ inθ g t gt t t gt x x ( in( co( +,x 45 + ( ( co( in t coθ inθ g Anwer (c

11 . A golf ball i launched at an angle with an initial peed of /, at an angle of 5 aboe the horizontal. The ball land on a green that i 5 aboe where the ball wa truck. How far ha the ball traeled in the horizontal direction by the tie it land? Firt draw a picture, then break the initial elocity into coponent:,x,y ( co( 5 ( in( Again we will ue projectile equation: x x a x x +,x,x t y y +,y, y,y gt t g gt ( y y V Uing y and y5 in the firt ertical equation, we can find the tie: y y t +,y t gt (.98 t.98t + 5 or t 4.46 t. 9.8 t Quadratic forula: t b ± b a 4ac The ball i at height 5 twice once on the way up, and then again on the way down. We want the 4.46 tie. x x x + + Anwer (a,x t ( 9.8 ( X? 5

12 . A golf ball i launched at an angle with an initial peed of /, at an angle of 5 aboe the horizontal. The ball land on a green that i 5 aboe where the ball wa truck. Find the elocity of the ball jut before it land. Thi proble can be done ery quickly with no calculation whatoeer if you think about the ituation and look at the poible anwer gien. You know the peed will be lower than the initial peed becaue the ball ha not yet returned to the initial height. Plu it i on the way down. The only anwer that fit i anwer (b. To calculate the anwer, firt break the initial elocity into coponent:,x,y ( co( 5 ( in( We need to find the coponent of the final elocity. We are ignoring air reitance, o we can aue that the x-coponent of the elocity doe not change. For the y-coponent, we can ue the rd of our projectile equation: ( y y y, y g y ( ( 5 y.74 5 The agnitude of the elocity i found ia the Pythagorean Theore: r ( (.74 final 8. Fro the diagra, or jut coon ene, the angle ut be below the horizontal (it i on the way down. If you want to do the angle calculation, jut ue the ae tangent forula fro preiou proble. Anwer (b

13 . A jet plane coe in for a downward die a hown in Figure.9. The botto part of the path i a quarter circle haing a radiu of curature of 5. According to edical tet, pilot loe concioune at an acceleration of 5.5g. At what peed will the pilot black out for thi die? The gien acceleration i 5.5g. Thi ean 5.5 tie the acceleration due to graity: The path of the airplane i circular, o the gien acceleration ut be centripetal (toward the center. We hae a forula for centripetal acceleration: a cent 5.9 r Anwer (a

14 . Two children are on a erry-go-round which pin at a rate of reolution eery 5 econd. Bobby i tanding at a poition that i.75 fro the center, and Cindy i.5 fro the center. Which tateent i true about their linear peed? a Their peed are equal b Bobby peed i twice Cindy peed. c Cindy peed i one-and-a-half tie Bobby peed. d Cindy peed i twice Bobby peed..5 We don t need to do a lot of calculation for thi one. Enough inforation i gien to find the peed of each child, but that i too uch effort. Undertanding the relationhip between angular peed and linear peed will ake thi proble ee eay. Both children are on the ae rotating object, o they ut hae the ae angular peed (they rotate at the ae rate. Howeer, Cindy i farther fro the center, o he ha to trael a larger ditance eery tie he goe around. That i, her linear peed ut be greater. Since he i twice a far fro the center, he ha to trael twice a far for each rotation, thu her peed i twice a fat. Anwer (d.75 Here i the plug-into-the-equation olution (you need to know the circuference of a circle i πr: di tance tie Bobby Cindy π 5 π 5 (.75 ( Cindy Bobby.88.94