Today: Review for Exam 1 Wednesday: Chapter 5

Transcription

1 Exam Informa+on 1/1/14 Wednesday 7:3 PM All Sec+ons à MPHY 25 (this room, 3 min a.er class ends) Dura+on à 1 hour 15 min Today: Review for Exam 1 Wednesday: Chapter 5 Ø Please return to the classroom 2 min aler class is dismissed and wait to be let into the room. Ø Know your instructor s name (S+egler) and your sec+on number (55-59). Ø Have your TAMU ID ready to show when turning in your exam. Ø Calculators are allowed, no pre- saved data on them, if you are caught using previously saved data it will be considered chea=ng and dealt with accordingly. Exam Structure Ø 5 mul+ple choice ques+on You do not need to show your work on these. There is no par+al credit. Ø 4 long problems The problems will be similar to homework problems of medium difficulty. There will be a mix of numeric and symbolic problems. Par+al credit is given, you must show your work clearly.

2 Problem 1 Find the magnitude and direc+on of the sum R of the three vectors shown in the figure. R = A + B + C The vectors have the following magnitudes: A = 5.m, B = 9.5m, and C = 6.m. Express the direc+on of the vector sum by specifying the angle it makes with the posi+ve x- axis, with the counterclockwise angles taken to be posi+ve.

3 Problem 2 x(t) = t 4 2t (in SI units) describes the posi+on of a par+cle moving along a line. (a) What is the average velocity between and 2 s? (b) What is v(t) (b) What is the accelera+on at t = 3 s? v = r 2 r 1 a = v 2 v 1 v = d r dt a= d v dt = d2 r dt 2 r(t) = r + t v(t) dt v(t) = v + t a(t) dt

4 Problem 3 A rocket is launched from rest on the ground with an constant upward accelera+on of 5 m/s 2. 6 s aler the launch the rocket s engine shuts down. What is the maximum height reached by the rocket? (Neglect air resistance.) r(t) = r + v t at2 v(t) = v + at v 2 x = v 2 x, +2a x (x x ) (and similarly for y and z) r(t) = r ( v i + v f )t

5 Problem 4 A ball is dropped (from rest) from a window at height h and is seen to reach the ground in a certain +me. The ball- dropper then climbs to a height 2h but wants the ball to reach the ground in the original +me. Find the velocity v that must be given to this ball to achieve the goal. r(t) = r + v t at2 v(t) = v + at v 2 x = v 2 x, +2a x (x x ) (and similarly for y and z) r(t) = r ( v i + v f )t

6 Problem 5 A basketball player releases the ball from a height h 1 at an angle θ and ini+al velocity v in an aeempt to put the ball into the basket which is at height h 2 and a horizontal distance d. Calculate the distance d if the ball is to make it into the basket. (find in terms of h 1, h 2, θ, and v ) r(t) = r + v t at2 v(t) = v + at v 2 x = v 2 x, +2a x (x x ) (and similarly for y and z) r(t) = r ( v i + v f )t ax 2 + bx + c = x = b ± b 2 4ac 2a

7 Problem 6 A daring 51N swimmer dives off a cliff with a running horizontal leap, as shown. What must her minimum speed just as she leaves the top of the cliff, v, so that she will miss the ledge at the boeom, which is 1.75m wide and 9.m below the top of the cliff. r(t) = r + v t at2 v(t) = v + at v 2 x = v 2 x, +2a x (x x ) (and similarly for y and z) r(t) = r ( v i + v f )t

8 Problem 7 A jet plane comes in for a downward dive. The boeom part of the path is a quarter circle having a radius of curvature of 35 m. According to medical tests, pilots lose consciousness at an accelera+on of 5.5 g. (a) At what speed (in m/s) will the pilot black out for this dive? (b) At what speed (in mph) will the pilot black out for this dive? a rad = v2 R

9 Problem 8 Passengers on a carnival ride move at constant speed in a horizontal circle of radius 14. m, making a complete circle in 1. s. (a) What is their accelera+on? (b) Draw the accelera+on vector at each point (A, B, C, D). (c) How would your answer in (b) change if the speed were not constant? (Explain in words and/or drawing) a rad = v2 R

10 Problem 8 cont. (b) Draw the accelera+on vector at each point (A, B, C, D). (c) How would your answer in (b) change if the speed were not constant? (Explain in words and/or drawing) a rad = v2 R

11 Problem 9 A plane is flying north at 2 m/s in gale- force winds of 35. m/s which are blowing in a direc+on 3. south of east. How far off course are they in the east- west direc+on aler 2. hrs? (P=plane, A=air, E=earth) v A/C = v A/B + v B/C v A/B = v B/A

12 Problem 1 In a triathlon, a contestant swims from start to finish in a +me T. In order to do so, the contestant has to swim against the flow of the river which has a constant speed V rela+ve to ground as shown. What is the x- component of the swimmer s velocity, v x, with respect to the water? x D &inish W swimmer s path V water start v A/C = v A/B + v B/C v A/B = v B/A

13 Problem 11 A rocket starts from rest and moves upward from the surface of the earth. For the first 1.s of its mo+on, the ver+cal accelera+on of the rocket is given by a y (t) = (2.8 m/s 3 )t, where the +y- direc+on is upward. (a) What is the height of the rocket above the surface of the earth at t = 1.s? (b) What is the speed of the rocket when it is 325 m above the surface of the earth? v = r 2 r 1 a = v 2 v 1 v = d r dt a= d v dt = d2 r dt 2 r(t) = r + t v(t) dt v(t) = v + t a(t) dt

14 Problem 11 - cont. (a) What is the height of the rocket above the surface of the earth at t = 1.s? (b) What is the speed of the rocket when it is 325 m above the surface of the earth? v = r 2 r 1 a = v 2 v 1 v = d r dt a= d v dt = d2 r dt 2 r(t) = r + t v(t) dt v(t) = v + t a(t) dt

15 Problem 12 The accelera+on of an object is given by a(t) = 2. m/s 2 + (.75 m/s 3 )t while moving in the x- direc+on. If its ini+al posi+on is x = 3. m and its ini+al velocity is zero, find the velocity and posi+on when t = 2.5 s. v = r 2 r 1 a = v 2 v 1 v = d r dt a= d v dt = d2 r dt 2 r(t) = r + t v(t) dt v(t) = v + t a(t) dt

16 Problem 12 cont. The accelera+on of an object is given by a(t) = 2. m/s 2 + (.75 m/s 3 )t while moving in the x- direc+on. If its ini+al posi+on is x = 3. m and its ini+al velocity is zero, find the velocity and posi+on when t = 2.5 s. v = r 2 r 1 a = v 2 v 1 v = d r dt a= d v dt = d2 r dt 2 r(t) = r + t v(t) dt v(t) = v + t a(t) dt