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Views: 5,515

One gallon of paint (volume

= 3.78 \times 1 0^{- 3} m^{3}

) covers an area of

25.0 m^{- 1}

. What is the thickness of the fresh paint on the wall?

Topic:

Physics

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Views: 5,660

An ore loader moves 1200 tons/h from a mine to the surface. Convert this rate to pounds per second, using 1 ton

=

2000 \mathrm{lb}$.

Topic:

Physics

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Views: 5,133

Assume it takes 7.00 min to fill a 30.0 -gal gasoline tank. (a) Calculate the rate at which the tank is filled in gallons per second. (b) Calculate the rate at which the tank is filled in cubic meters per second. (c) Determine the time interval, in hours, required to fill a

1.00 - m^{3}

volume at the same rate. (1 U.S. gal

= 231

^{3}

Topic:

Physics

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Views: 5,992

The polar coordinates of a point are

r = 5.50 m

θ = 24 0^{\circ} .

What are the Cartesian coordinates of this point?

Topic:

Physics

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Views: 5,572

A fly lands on one wall of a room. The lower-left corner of the wall is selected as the origin of a two-dimensional Cartesian coordinate system. If the fly is located at the point having coordinates (2.00,1.00)

m

(a) how far is it from the origin?(b) What is its location in polar coordinates?

Topic:

Physics

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Views: 5,941

A plane flies from base camp to Lake

A, 280 km

away in the direction

20. 0^{\circ}

north of east. After dropping off supplies, it flies to Lake

B

190 km

30. 0^{\circ}

west of north from Lake A. Graphically determine the distance and direction from Lake

B

to the base camp.

Topic:

Physics

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Views: 5,562

A roller-coaster car moves 200 ft horizontally and then rises

135 ft

30. 0^{\circ}

above the horizontal. It next travels 135 ft at an angle of

40. 0^{\circ}

downward. What is its displacement from its starting point? Use graphical techniques.

Topic:

Physics

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Views: 5,371

Given the vectors

A = 2.00 \hat{i} + \underline{6.00} \hat{j}_{1}

B = 3.00 \hat{i} -

2.00 \hat{j}, (a)

draw the vector

sum C = A + B

and the vectordifference

D = A - B

. (b) Calculate

C

D,

in terms of unit vectors. (c) Calculate

C

D

in terms of polar coordinates, with angles measured with respect to the positive

x

Topic:

Physics

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Views: 5,244

taking A = (6.00 \hat{i} - 8.00 \hat{j})

B = (- 8.00 \hat{i} +

3.00 \hat{j})

C = (26.0 \hat{i} + 19.0 \hat{j})

units, determine

a

b

a A + b B + C = 0.

(b) A student has learned that a single equation cannot be solved to determine values for more than one unknown in it. How would you explain to him that both

a

b

can be determined from the single equation used in part (a)?

Topic:

Physics

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Question 10

Views: 5,956

A

x, y,

z

components of 8.00,12.0 and -4.00 units, respectively. (a) Write a vector expression for

A

in unit-vector notation. (b) Obtain a unit-vector expression for a vector

B

one-fourth the length of

A

pointing in the same direction as A. (c) Obtain a unit-vector expression for a vector

C

three times the length of

A

pointing in the direction opposite the direction of

A

Topic:

Physics

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Question 11

Views: 5,885

Consider the two vectors

A = 3 \hat{i} - 2 \hat{j}

B = - \hat{i} - 4 \hat{j}

(a) A + B, (b) A - B, (c) ∣ A + B ∣, (d) ∣ A - B ∣

and (e) the directions of

A + B

A - B

Topic:

Physics

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Question 12

Views: 5,013

In physics, it is important to use mathematical approximations. (a) Demonstrate that for small angles

(< 2 0^{\circ})

tan α \approx sin α \approx α = \frac{π α ^{'}}{18 0 ^{\circ}}

α

is in radians and

α^{'}

is in degrees. (b) Use a calculator to find the largest angle for which tan

α

may be approximated by

α

with an error less than

10.0%

Topic:

Physics

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Question 13

Views: 5,033

A

B

have precisely equal magnitudes. For the magnitude of

A + B

to be 100 times larger than the magnitude of

A - B,

what must be the angle between them?

Topic:

Physics

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Question 14

Views: 5,912

The helicopter view in Fig. P1.67 shows two people pulling on a stubborn mule. The person on the right pulls with a force

F_{1}

120 N

and direction of

θ_{1} =

60. 0^{\circ} .

The person on the left pulls with a force

F_{2}

of magnitude 80.0

N

and direction of

θ_{2} = 75. 0^{\circ} .

Find (a) the single force that is equivalent to the two forces shown and (b) the force that a third person would have to exert on the mule to make the resultant force equal to zero. The forces are measured in units of newtons (symbolized N).

Topic:

Physics

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Question 15

Views: 5,101

A woman wishing to know the height of a mountain measures the angle of elevation of a mountaintop as

12. 0^{\circ}

1.00 km

closer to the mountain on level ground, she finds the angle to be

14. 0^{\circ} .

(a) Draw a picture of the problem, neglecting the height of the woman's eyes above the ground. Hint: Use two triangles. (b) Using the symbol

y

to represent the mountain height and the symbol

x

to represent the woman's original distance from the mountain, label the picture. (c) Using the labeled picture, write two trigonometric equations relating the two selected variables. (d) Find the height

y

Topic:

Physics

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Question 16

Views: 5,885

You stand in a flat meadow and observe two cows (Fig.

P 1.70

A

is due north of you and 15.0 m from your position. Cow B is

25.0 m

from your position. From your point of view, the angle between cow

A

cow B

20. 0^{\circ},

B

appearing to the right of cow A. (a) How far apart are cow A and cow B? (b) Consider the view seen by cow A. According to this cow, what is the angle between you and cow B? (c) Consider the view seen by cow B. According to this cow, what is the angle between you and cow A? Hint: What does the situation look like to a hummingbird hovering above the meadow? (d) Two stars in the sky appear to be

20. 0^{\circ}

apart. Star A is 15.0 ly from the Earth, and star

B

, appearing to the right of star

A

, is 25.0 ly from the Earth. To an inhabitant of a planet orbiting star

A

, what is the angle in the sky between star

B

Sun

Topic:

Physics

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Question 17

Views: 5,981

The position of a particle moving along the

x

axis varies in time according to the expression

x = 3 t^{2}

x

is in meters and

t

is in seconds. Evaluate its position

(a)

t = 3.00 s

3.00 s + Δ t .

(c) Evaluate the limit of

Δ x /Δ t

Δ t

approaches zero to find the velocity at

t = 3.00

Topic:

Physics

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Question 18

Views: 5,193

(a) Use the data in Problem 2.3 to construct a smooth graph of position versus time. (b) By constructing tangents to the

x (t)

curve, find the instantaneous velocity of the car at several instants. (c) Plot the instantaneous velocity versus time and, from this information, determine the average acceleration of the car. (d) What was the initial velocity of the car?

Topic:

Physics

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Question 19

Views: 5,616

P 2.15

shows a graph of

v_{x}

t

for the motion of a motorcyclist as he starts from rest and moves along the road in a straight line. (a) Find the average acceleration for the time interval

t = 0

t = 6.00

s. (b) Estimate the time at which the acceleration has its greatest positive value and the value of the acceleration at that instant.(c) When is the acceleration zero? (d) Estimate the maximum negative value of the acceleration and the time at which it occurs.

Topic:

Physics

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Question 20

Views: 5,263

Draw motion diagrams for (a) an object moving to the right at constant speed, (b) an object moving to the right and speeding up at a constant rate, (c) an object moving to the right and slowing down at a constant rate, (d) an object moving to the left and speeding up at a constant rate, and (e) an object moving to the left and slowing down at a constant rate. (f) How would your drawings change if the changes in speed were not uniform, that is, if the speed were not changing at a constant rate?

Topic:

Physics

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