Homework 4
Due in class (1:00pm) on Thursday of Week 5 (Feb. 6, 2003)
Non-Textbook Problems
A. (i) Explain the difference between velocity and acceleration. (ii) If an object travels with a constant velocity, what do we know about its acceleration?

B. Match each of the following statements will one or more of the equations of kinematics in one dimension (p. 38):
(i) The final velocity of an object experiencing constant acceleration depends upon the initial velocity and the acceleration.
(ii) The displacement of an object experiencing constant acceleration is equal to the average velocity of the object times the time elapsed.
(iii) If the displacement of an object experiencing constant acceleration is plotted versus time, the function is parabolic, with the exact shape determined by the initial velocity and the acceleration.

C. For the case of projectile motion, derive an equation expressing the vertical displacement, y, as a function of: the horizontal displacement, x; the acceleration due to gravity, g; and the x and y components of the initial velocity. (HINT: Which variable do x and y have in common?) Graph this function assuming that the x and y components of the initial velocity are positive.

Textbook Problems, Chapter 3
Conceptual Questions (p. 77): 7, 10
Problems (p. 78): 13, 17, 67

Brief Answers
Non-Textbook Problems
A. (i) The velocity of an object includes its speed and direction. Acceleration is the change in velocity. (ii) If velocity is constant, acceleration is 0.
B. (i) v=vo+at and v2=vo2+2ax (ii) x=(1/2)(vo+v)t  (iii) x=vot+(1/2)at2
C. y = (-g/(2vox2))x2 + (voy/vox)x
This parabola opens down, crosses the x-axis at 0 and 2voxvoy/g, and has a vertex at (voxvoy/g, voy2/(2g)).

Textbook Problems, Chapter 3
Conceptual Questions
7. Yes. If the boat is at rest, the wrench falls directly below where it was dropped. If the boat is moving with constant velocity, the wrench is given a velocity in the x direction, but takes the same time to fall as before. Its movement in the x direction exactly matches the boat's movement, so it hits in the same place. (I've ignored air resistance.)
10. (a) Displacement is different. The stone that is thrown includes both an x and y component of displacement, so total displacement is larger.
(b) Speed just before impact is different. The stone that is thrown includes both x and y components of velocity, so impact speed will be greater.
(c) Time of flight is the same. It depends only on the y component of the motion, which is the same for the two cases.

Problems
13. 4.4 s
17. 14.1 m/s
67. 15.7 degrees