CH.1& 2 VECTORS & 1D KINEMATICS (General Physics)

Physics 140 ch.1 Vectors

2.23MB

 

 

Physics 140 ch.2 Kinematics

3.71MB

[HW]

<Ch1. Vectors>

1.shows the components of F-> , Fx and Fy , along the x and y axes of the coordinate system, respectively. The components of a vector depend on the coordinate system's orientation, the key being the angle between the vector and the coordinate axes, often designated θ .
θtheta is measured to the vector from the x axis, and counterclockwise is positive.

Express Fx and Fy in terms of the length of the vector F and the angle θ, with the components separated by a comma.

 

Answer: Fx, Fy = Fcos θ, Fsin θ

 

 

 

2.  (A) Which of the following procedures will add the vectors A→ and B→?

Answer: Put the tail of B→ on the arrow of A→; C→ goes from the tail of⃗ A→ to the arrow of B→

(B) Find C, the length of⃗ C→, the sum of A→ and B→.Find CCC, the length of⃗ C→, the sum of A→an⃗ B→B.

Answer:

(C) Find the angle ϕ that the vector C→ makes with vector A→.

Express ϕ in terms of C and any of the quantities given in the problem introduction ( A, B, and/or θ) as well as any necessary constants. Use radian measure for known angles. Use asin for arcsine.

 

 

Answer:

(D) To manipulate these vectors using vector components, we must first choose a coordinate system. In this case choosing means specifying the angle of the x axis. The y axis must be perpendicular to this and by convention is oriented π/2 radians counterclockwise from the x axis.
Indicate whether the following statement is true or false:
There is only one unique coordinate system in which vector components can be added.
Answer: False

(E) The key point is that you are completely free to choose any coordinate system you want in which to manipulate the vectors. It is a matter of convenience only, and so you must consider which orientation will simplify finding the components of the given vectors and interpreting the results in that coordinate system to get the required answer. Considering these factors, and knowing that you are going to be required to find the length of C→ and its angle with respect to A→, which of the following orientations simplifies the calculation the most?
Answer: The x axis should be oriented along A→.


(F) Find the components of B→ in the coordinate system shown. Express your answer as an ordered pair: x component, y component ; in terms of B and θ. Use radian measure for known angles.

Answer: Bx, By = Bcosθ, Bsinθ.

(G) In the same coordinate system, what are the components of C→?

Express your answer as an ordered pair separated by a comma. Give your answer in terms of variables defined in the introduction ( A, B, and θ). Use radian measure for known angles.

 

Answer: Cx, Cy = A + Bcosθ, Bsinθ.

 

3. Let vectors A =(2,1,−4), B =(−3,0,1), and C =(−1,−1,2).
Calculate the following:

(F) Express your answer in terms of V1

(G) If V1 and V2 are perpendicular,

(H) If V1 and V2 are parallel, (express your answer in terms of V1 and V2.)

4. Let vectors A=(1,0,−3), B =(−2,5,1), and C =(3,1,1).
Calculate the following, expressing your answers as ordered triples (three comma-separated numbers).

 

5. Let vectors A =(2,−1,1), B =(3,0,5), and C =(1,4,−2), where (x,y,z) are the components of the vectors along i^, j^, and k^ respectively. Calculate the following:

(A) Express your answer as an ordered triplet of components (x,y,z) with commas to separate the components.

(B) Express your answer as an ordered triplet |A|,|B|,|C||A→|,|B→|,|C→| with commas to separate the magnitudes, to three significant figures.

(D) Determine the angle θ between B→ and C→. Express your answer numerically in radians, to two significant figures.

 

 

(E) Express your answer as an ordered triplet of components  (x,y,z)  with commas to separate the components.

 

6. You are given vectors A = 5.3 i^− 6.9 j^ and B = 3.9 i^+ 7.1 j^. A third vector C  lies in the xy-plane. Vector C  is perpendicular to vector A and the scalar product of C with B is 20.0.

 

(A) Find the x -component of vector C

 

(B) Find the yy-component of vector C→.

<Ch.2 1D Kinematics> 

7. Two cars travel on the parallel lanes of a two-lane road. The cars’ motions are represented by the position versus time graph shown in the figure. Answer the questions using the times from the graph indicated by letters.

(A) At which of the times do the two cars pass each other?
Answer: D
(B) Are the two cars traveling in the same direction when they pass each other?
Answer: No
(C) At which of the lettered times, if any, does car #1 momentarily stop?
Answer: None
(D) At which of the lettered times, if any, does car #2 momentarily stop?
Answer: C
(E) At which of the lettered times are the cars moving with nearly identical velocity?
Answer: A

8. The motions described in each of the questions take place at an intersection on a two-lane road with a stop sign in each direction. For each motion, select the correct position versus time graph. For all of the motions, the stop sign is at the position x=0, and east is the positive x direction.

(A) A driver ignores the stop sign and continues driving east at constant speed.
Answer: D
(B is incorrect.)

 

(B) A driver ignores the stop sign and continues driving west at constant speed.
Answer: A
(C) A driver, traveling west, slows and stops at the stop sign.
Answer: F
(D) A driver, after stopping at the stop sign, travels east with a positive acceleration.
Answer: E

9. A woman stands at the edge of a cliff, holding one ball in each hand. At time t0, she throws one ball straight up with speed v0 and the other straight down, also with speed v0.

(A)If the ball that is thrown downward has an acceleration of magnitude a at the instant of its release (i.e., when there is no longer any force on the ball due to the woman's hand), what is the relationship between a and g , the magnitude of the acceleration of gravity?
Answer: a=g
(B) Which ball has the greater acceleration at the instant of release?
Answer: Neithger; the accelerations of both balls are the same.
(C) Which ball has the greater speed at the instant of release?
Answer: Neither; the speeds are the same.
(D) Which ball has the greater average speed during the 1-s interval after release (assuming neither hits the ground during that time)?
Answer: the ball thrown downward
(E) Which ball hits the ground with greater speed?
Answer: Neither, the balls hit the ground with the same speed.

10. In this problem, you will apply kinematic equations to a jumping flea. Take the magnitude of free-fall acceleration to be 9.80 m/s2 . Ignore air resistance.
(A) A flea jumps straight up to a maximum height of 0.510 mm . What is its initial velocity v0v0v_0 as it leaves the ground? Express your answer in meters per second to three significant figures.
Answer: v0 = 3.16 m/s

(B) How long is the flea in the air from the time it jumps to the time it hits the ground?
Express your answer in seconds to three significant figures.
Answer: Time in air = 0.645 s

11. The engineer of a passenger train traveling at 25.0 m/s sights a freight train whose caboose is 200 m ahead on the same track. The freight train is traveling at 15.0 m/s in the same direction as the passenger train. The engineer of the passenger train immediately applies the brakes, causing a constant acceleration of -0.100 m/s2, while the freight train continues with constant speed. Take x=0 at the location of the front of the passenger train when the engineer applies the brakes.

(A) Will the cows nearby witness a collision?
Answer: Yes .
(B) If so, where will it take place? Express your answer in meters.
Answer: x = 538 m

 

12. You are on the roof of the physics building, 46.0 m above the ground. Your physics professor, who is 1.80 m tall, is walking alongside the building at a constant speed of 1.20 m/s.

(A) If you wish to drop an egg on your professor's head, how far from the building should the professor be when you release the egg? Assume that the egg is in free fall. Express your answer in meters.
Ansewr: 3.60 m