{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Chap 03 Solutions copy

# Chap 03 Solutions copy - VECTORS AND MOTION IN TWO...

This preview shows pages 1–3. Sign up to view the full content.

3-1 V ECTORS AND M OTION IN T WO D IMENSIONS 3 Q3.1. Reason: (a) If one component of the vector is zero, then the other component must not be zero (unless the whole vector is zero). Thus the magnitude of the vector will be the value of the other component. For example, if A x = 0 m and A y = 5 m, then the magnitude of the vector is A = (0 m) 2 + (5 m) 2 = 5 m (b) A zero magnitude says that the length of the vector is zero, thus each component must be zero. Assess: It stands to reason that a vector can have a nonzero magnitude with one component zero as long as the other one isn’t. It also makes sense that for the magnitude of the vector to be zero all the components must be zero. Q3.2. Reason: No, it is not possible. A scalar has a magnitude only but a vector has direction as well. Even if each has the same dimensions, the result of the addition of a scalar and a vector is ambiguous. Assess: We already learned in chapter 1 that we can’t add quantities unless they have the same dimensions; here we also point out that two quantities that will be added (or subtracted) must both be scalars or both vectors. Q3.3. Reason: Consider two vectors ! A and ! B . Their sum can be found using the method of algebraic addition. In Question 3.2 we found that the components of the zero vector are both zero. The components of the resultant of ! A and ! B must then be zero also. So R x = A x + B x = 0 R y = A y + B y = 0 Solving for the components of ! B in terms of ! A gives B x = ! A x and B y = ! A y . Then the magnitude of ! B is ( B x ) 2 + ( B y ) 2 = ( ! A x ) 2 + ( ! A y ) 2 = ( A x ) 2 + ( A y ) 2 . So then the magnitude of ! B is exactly equal to the magnitude of ! A . Assess: For two vectors to add to zero, the vectors must have exactly the same magnitude and point in opposite directions. Q3.4. Reason: (a) C = A + B only if ! A and ! B are in the same direction. Size does not matter. (b) C = A B if ! A and ! B are in the opposite direction to each other. Size matters only in that A > B because C as a magnitude can only be positive. Assess: Visualize the situation with arrows.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
3-2 Chapter 3 Q3.5. Reason: The ones that are constant are v x , a x , and a y . Furthermore, a x is not only constant, it is zero. Assess: There are instants when other quantities can be zero, but not throughout the flight. Remember that a y = g throughout the flight and that v x is constant; that is, projectile motion is nothing more than the combination of two simple kinds of motion: constant horizontal velocity and constant vertical acceleration. Q3.6. Reason: The acceleration of the ball is due to gravity, so the acceleration the ball experiences is always straight downward. (a) The velocity vector of the ball always has a component in the horizontal direction since it was thrown at an angle of 40 ° . The horizontal component of the ball’s velocity is constant throughout its trajectory. Since the velocity vector always has a component in the horizontal direction, it is never pointing entirely straight up or down.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern