Physics 121 Homework for Exam #1

Assignment #1 Textbook Sections 1-4 & 1-5 Date Due: Wed. Jan. 8
Assignment #2 Textbook Sections 1-2 & 1-3 Date Due: Fri. Jan. 10
Assignment #3 Textbook Section 2-1 Date Due: Mon. Jan. 13
Assignment #4 Textbook Sections 2-2 & 2-3 Date Due: Tue. Jan. 14
Assignment #5 Textbook Section 2-3 Date Due: Wed. Jan.15
Assignment #6 Textbook Sections 3-1 to 3-3 Date Due: Fri. Jan. 17
Assignment #7 Textbook Section 3-4 Date Due: Tue. Jan. 21
Assignment #8 Textbook Sections 3-3 Date Due: Wed. Jan. 22

START for EXAM #1 CHAPTER 1
**** Please Do Not Turn in Homework Papers with Ragged Edges ****
Assignment #1
Textbook Sections 1-4 & 1-5
Date Due: Wed. Jan. 8

1-1. Express the following numbers rounded to 3 Significant Figures:
(A) Sidereal Year = 365.25636 mean solar days.
(B) Density of water (at 4oC) = 0.999972 g/cm3.
(C) Speed of light (vacuum)= 2.99792457x108 m/s.
(D) 99 miles = 522,720 ft
1-2. State the number of significant figures in the following numbers
(A) 1.44 ms
(B) .00000144 s
(C) 1.004 s
(D) 410.0 s
(E) 5.205x10-6s
1-3. Calculate the following expressions and express your answer to the number of significant digits indicated:       
(A) (6.555)π = ? Rounded to 3 Significant Figures
(B) (9.801)sin(45.70o) = ? Rounded to 2 Significant Figures
(C) (24.56)2/(82.90x10-3) = ? Rounded to 4 Significant Figures
(D) 2π tan2(1.32 rad) = ? Rounded to 4 Significant Figures
(E) 78.56345 - 78.54622 = ? Rounded to 2 Significant Figures

Unless otherwise requested, for the rest of the quarter express your answers on all subsequent homework problems rounded to three Significant Figures.
Assignment #2
Textbook Sections 1-2 & 1-3
Date Due: Fri. Jan. 10
2-1. The maximum highway speed limit in some States is 75.0 mph, miles per hour. Convert this speed to the following units:
(A) km/h.
(B) m/s.
(C) ft/min.
(D) mm/μs.
2-2. Determine the units that the quantities a and b must have if the following expressions are going to be dimensionally correct.
(A) when x in cm, t in s
(B) when x in km, t in s
(C) when v in km/s, t in ms
(D) when v in cm/s, t in s
(E) when x in m, v in m/s, and t in s

HOMEWORK for CHAPTER 2
Assignment #3 Textbook Sections 2-1 Date Due: Mon. Jan. 13
3-1. A Jogger runs in a straight line at a speed of 6.25 m/s for 7.50 min and then runs at 4.40 m/s for the next 11.8 min in the same direction.
(A) What is the total distance in km covered by the jogger ?

(B) What is the jogger’s average speed in m/s during the run ?

3-2. Moving in a straight line, an object's position as a function of time is given by: (Calculus of Motion)
x (t) = a(t - t)2 + b where a = 3.50 m/s2, b = 4.00 m, t = 2.00 s
{x(t) = a(t 2- t 2) + b t where a = 1.90 m/s2, b = 6.50 m/s, t = 4.00 s}

See Section 5. BRACES "{NUMBERS}" in the
Overview of the Daily Homework
for information about the numbers in {}.
(A) Plot the object's position as a function of time.

(B) Calculate the object's initial position at t = 0, how far is the object from its starting position after 5.80 seconds, and how far has it traveled in the 5.80 sec.
Ans: {-30.4 m, 102 m, 102 m Note these two last answers are not the same in the non-bracketed problem you turn in.}

BONUS:
(C) What is the object's average velocity between t = 0 and t = 4.00 s ?
Ans: { vav = 14.1 m/s}

Assignment #4 Textbook Sections 2-2 & 2-3 Date Due: Tue. Jan. 14
4-1. A car moving at 85.0 km/h {98.5 km/h} brakes to a halt in 9.30 seconds.
(A) What was the car's average acceleration while it was stopping ?
Ans:{-2.94 m/s2}

(B) If the car went 110 meters {128 m} before it came to a halt, could the car's acceleration be constant. Hint: Calculate the distance the car would travel before stopping if the acceleration were constant.
Ans: {No, it would go 127 m}

4-2. Moving in a straight line, an object's position as a function of time is given by: (
x (t) = a(t - t)2 + b where a = 3.50 m/s2, b = 4.00 m, t = 2.00 s
{x(t) = a(t 2- t 2) + b t where a = 1.90 m/s2, b = 6.50 m/s, t = 4.00 s}
Calculus of Motion)
(A) Using differential calculus, determine the equation for the object's velocity as a function of time and sketch the v versus t plot.
Ans: {v(t) = 2a t + b}

(B) What is the object's instantaneous velocity at the times t = 0, t = 2.00 s, and t = 4.00 s ?
Ans: {6.50 m/s, 14.1 m/s, 21.7 m/s}

(C) Using differential calculus, show that this object moves at a constant acceleration, and determine the value of the object's acceleration.
Ans: {a = 3.80 m/s 2}

Assignment #5 Textbook Section 2-3 Date Due: Wed. Jan.15
5-1. A speedboat increases its speed uniformly from 18.0 m/s to 79.0 m/s over a distance of 2.10 km {1.40 km}. (Constant Acceleration)
(A) What is the magnitude of the boat's acceleration ?
Ans: {2.11 m/s2}
(B) How much time did it take the boat to increase its speed ?
Ans: {28.9 s}

5-2. A ball is projected from ground level, vertically upwards at a speed of 62.5 m/s {25.0 m/s}. Neglecting air resistance, (Free-Fall)

(A) how long will it take the ball to reach its highest point after it leaves the ground?
Ans: {2.55 s}
(B) how high will the ball rise ?
Ans: {31.9 m}
(C) what will be the ball's height 3.50 seconds after it is launched upward ?
Ans: {27.5 m}

(D) how fast (and in which direction) will the ball be moving 3.10 seconds after it is launched ?
Ans: {5.38 m/s, downwards}

HOMEWORK for CHAPTER 3

Assignment #6 Textbook Sections 3-1 to 3-3 Date Due: Fri. Jan. 17
6. A jogger runs 1.30 km on a heading of 23.0o South of due East {23.0o West of due North}. The jogger then turns and runs 2.60 km due North. Assume that the positive x-axis is due East and the positive y-axis is due North. (Vector Addition)
(A) Sketch the vectors associated with the jogger's movement.

(B) What are the components of the jogger's final displacement vector relative to the starting position ?
Ans: { x = -.508 km, y = 3.80 km}
(C) What is the magnitude and direction of the jogger's final displacement vector, i.e. how far is the jogger from the starting position and in what direction is the jogger's heading relative to due East ? Ans: {3.83 km, 97.6o N of E}

(D) If at the start, the jogger first runs 2.60 km due North and then runs 1.30 km on a heading of 23.0o S of E {23.0o W of N}, what is the magnitude and direction of the jogger's displacement vector relative to due East ? Ans:{?}

BONUS:
(E) For the original problem, if on the second leg, the jogger runs 2.60 km at an angle of 38.0o West of due North {38.0o N of E} instead of just due North, what is the magnitude and direction of the jogger's displacement vector relative to due East ?
Ans: {3.19 km, 61.2o N of E}

Men love to wonder, and that is the seed of Science
RALPH WALDO EMERSON

Assignment #7 Textbook Section 3-4 Date Due: Tue. Jan. 21

7-1. A plane has a flying speed of 220 km/hr {180 km/hr} in still air. The plane takes off on a heading of 58.0o N of E. There is a wind blowing from due West at 65.0 km/hr. (Relative Velocity)
(A) At what angle relative to due East will the plane be observed to travel when observed from the ground ?
Ans:{43.5o N of E}

(B) How far will the plane be from its starting point after 58.0 minutes ?
Ans:{214 km}

7-2. A person in a boat capable of traveling at 13.0 km/h {11.5 km/h} in still water wishes to travel directly across a river that is flowing at 5.70 km/h {3.40 km/h} and is 34.0 m {150 m} wide.

(A) At what angle, relative to a line straight across the river, would the boat have to heading in order that its physical path is in a straight line directly across from the boat's launching location ? Sketch the boat's path and label the angle found. Ans: {q = 17.2o}
(B) How long would it take the boat to cross the river under these conditions ?
Ans: {49.2 s}

BONUS:
(C) If the boat heads upstream against the flow of the river at an angle of 30.0o relative to the bank, at what speed and at what angle relative to the bank will the boat be observed to actually move by someone standing on the bank ?
Ans: {8.72 km/h at 41.2o}

Assignment #8 Textbook Sections 3-3 Date Due: Wed. Jan. 22
8-1. A ball is thrown horizontally from the top of a building 65.0 m {35 m} high. The ball strikes the ground 85.0 m {80.0 m} from the base of the building. (Projectile Motion)
(A) How long is the ball in flight ?
Ans: {2.67 s}
(B) What are the horizontal and vertical components of the ball's velocity just as it strikes the ground ?
Ans: { vx = 29.9 m/s, vy = -26.2 m/s}
(C) How fast and at what angle does the ball strike the ground? Sketch your answer.
Ans: { v = 39.8 m/s, q = -41.2.0o}
8-2. A punter kicks a football at an angle of 48.0o relative to the ground. The football is observed to move horizontally at a speed of 19.0 m/s {27.6 m/s}. Neglecting air resistance,
(A) what is the initial velocity of the football just after it leaves the punter's foot ?
Ans: { vo = 41.2 m/s}
(B) to what height will the football rise ?
Ans: {47.9 m}

(C) how long will the football be in the air if it hits the ground ?
Ans: {6.26 s}

(D) how far does the football travel horizontally if it hits the ground ?
Ans: {173 m}

After grading Assignment #8, I will place it (along with any old assignments you have not picked up) outside my office by Wednesday afternoon.


FIRST EXAM

Friday January 24
CHAPTERS 1, 2, & 3

Conversion of Units & Significant Figures
Average & Instantaneous Velocity
Average & Instantaneous Acceleration
Magnitude & Direction, Components of Vectors
Addition and Scalar Product of Vectors
Projectile Motion
Relative Velocities


There are two way to slide easily through life:
to believe everything or to doubt everything. Both ways save us from thinking.
ALFREAD KORZYBSKI