1. Physics 218: Mechanics Instructor: Dr. Tatiana Erukhimova Sections 807, 808, 809 Lecture 5

2. Overview of Today’s Class Hw Quiz Vectors

3. A ball is thrown vertically upward with a velocity of magnitude v 1 from a window at height H. In addition to gravity acting on the ball there is another force so that the acceleration in the up direction is –g+  t where  is a constant and t is the time. What is the ball’s position when the acceleration is zero?

4. Falling with air resistance

5. A rocket, initially at rest, is fired at t=0 vertically down from a building of height H. The rocket’s acceleration, including the effects of gravity, is downwards with increasing magnitude given by a(t)=  t, where  is a known constant. When does it hit the ground and how fast is it going when it hits?

6. 16 m You want to measure the height of a building. You stand 2m away from a 3m pole and see that it’s “in line” with the top of the building. You measure 16 m from the pole to the building. What is the height of the building?

7. Adding Vectors by Components 1.Draw a diagram 2.Choose x and y axes. Choose them in a way that make your work easier. (E.g. choose one axis along the direction of one of the vectors so that the vector will have only one component). 3.Resolve each vector in x and y components 4.Calculate each component using sine and cosine. Be careful with signs: any component that points along the negative x or y axis gets a negative sign. 5.Add the x components together to get the x component of the resultant. Similar for y: V x =V 1x +V 2x +… V y =V 1y +V 2y +…

8. 6. If you want to know the magnitude and direction of the resultant vector,

9. CRAYFISH, SWAN, AND PIKE (Translation of I. Krylov's fable) Let crayfish, swan and pike Draw heavy loaded cart, Each being just a part Of harness they dislike. They try a lot, and everyone Starts pulling it with zeal; The problem is that each of them With his path wants to deal! The swan makes upward for a cloud, The crayfish falls behind; The pike dives sharply in the deep, And cart moves not from site. The moral of the verse is that Accordance should prevail Amid the people who have plans To work but not in vain.

10. Russian fable: Swan, Crawfish, and Pike Lake FcFc FpFp River FsFs Find F s and F c if F p, θ, and  are given Despite their huge effort the box does not move!

11. Given two vectors, and a) find the magnitude of each vector b) Write an expression for the vector difference using unit vectors

12. Given two vectors, and a) Find the components of the vector b) Find the magnitude of and the tangent of the angle makes with the x axis. Quiz

13. a) Express the vectors,, and in terms of their components. y x b) Find the components of the fourth force, that should be added for the object to be in static equilibrium.

14. A cannon at the origin points up at an angle θ with the x axis. A shell is fired which leaves the barrel with a velocity of magnitude V m. a)When does the shell reach its maximum height? b)What is the maximum height? c)What is the range (horizontal distance)? d)What is the velocity of the shell when it hits the ground?

15. Have a great day! Hw: All Chapters 3 and 4 problems and exercises