College Physics
10th Edition
ISBN: 9781285737027
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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Question
Chapter 1, Problem 50P
To determine
The general equation for the height of mountain.
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A woman wishing to know the height of a mountain measures the angle of elevation of the mountaintop as 12.0°. After walking 1.00 km closer to the mountain on level ground, she finds the angle to be 14.0°. (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.
During a visit to New York City, Lil decides to estimate the height of the Empire State Building (see figure below). She measures the angle ? of elevation of the spire atop the building as 19°. After walking x = 9.42 ✕ 102 ft closer to the iconic building, she finds the angle to be 24.0°. Use Lil's data to estimate the height h of the Empire State Building. (Enter your answer to at least the nearest foot.)
Given:
JA = 19.3
10A = 29.1°
B: B₂ = 35.7, By = -48.6
(a) Calculate the x-components and y-components of Ã.
A₂ =
Ā:
Ay =
4.
(b) Calculate the length and direction of B.
Assume angles are measured from the +x-axis with counter-clockwise as positive angles and clockwise as negative angles.
B =
0.
0
OB=
(c) Calculate the components of the vector sum of à + B = Č:
C₁=
0c=
Cy=
4.
(d) Calculate the length and direction of C:
Assume angles are measured from the +x-axis with counter-clockwise as positive angles and clockwise as negative angles.
C=
0
Chapter 1 Solutions
College Physics
Ch. 1 - Math Review Convert the following numbers to...Ch. 1 - Math Review Simplify the following expression in...Ch. 1 - Simplify the following expression, combining terms...Ch. 1 - The Roman cubitus is an ancient unit of measure...Ch. 1 - A house is advertised as having 1 420 square feet...Ch. 1 - A rectangular airstrip measures 32.30 m by 210 m,...Ch. 1 - Use the rules for significant figures to find the...Ch. 1 - Find the polar coordinates corresponding to a...Ch. 1 - Prob. 9WUECh. 1 - Estimate the order of magnitude of the length, in...
Ch. 1 - What types of natural phenomena could serve as...Ch. 1 - Find the order of magnitude of your age in...Ch. 1 - An object with a mass of 1 kg weighs approximately...Ch. 1 - (a) Estimate the number of times your heart beats...Ch. 1 - Estimate the number of atoms in 1 cm5 of a solid....Ch. 1 - The height of a horse is sometimes given in units...Ch. 1 - Prob. 9CQCh. 1 - Why is the metric system of units considered...Ch. 1 - How can an estimate be of value even when it is...Ch. 1 - Suppose two quantities, A and B, have different...Ch. 1 - Answer each question yes or no. Must two...Ch. 1 - The period of a simple pendulum, defined as the...Ch. 1 - (a) Suppose the displacement of an object is...Ch. 1 - A shape that covers an area A and has a uniform...Ch. 1 - Each of the following equations was given by a...Ch. 1 - Prob. 5PCh. 1 - Kinetic energy KE (Topic 5) has dimensions kg ...Ch. 1 - A carpet is to be installed in a room of length...Ch. 1 - Prob. 8PCh. 1 - How many significant figures are there in (a) 78.9...Ch. 1 - The speed of light is now defined to be 2.997 924...Ch. 1 - A block of gold has length 5.62 cm. width 6.35 cm,...Ch. 1 - The radius of a circle is measured to be (10.5 ...Ch. 1 - The edges of a shoebox are measured to be 11.4 cm,...Ch. 1 - Carry out the following arithmetic operations: (a)...Ch. 1 - A fathom is a unit of length, usually reserved for...Ch. 1 - A small turtle moves at a speed of 186 furlongs...Ch. 1 - A firkin is an old British unit of volume equal to...Ch. 1 - Find the height or length of these natural wonders...Ch. 1 - A car is traveling at a speed of 38.0 m/s on an...Ch. 1 - A certain car has a fuel efficiency of 25.0 miles...Ch. 1 - The diameter of a sphere is measured to be 5.36...Ch. 1 - Suppose your hair grows at the rate of 1/32 inch...Ch. 1 - The speed of light is about 3.00 108 m/s. Convert...Ch. 1 - A house is 50.0 ft long and 26 ft wide and has...Ch. 1 - The amount of water in reservoirs is often...Ch. 1 - The base of a pyramid covers an area of 13.0 acres...Ch. 1 - A quart container of ice cream is to be made in...Ch. 1 - Estimate the number of steps you would have to...Ch. 1 - Estimate the number of breaths taken by a human...Ch. 1 - Estimate the number of people in the world who are...Ch. 1 - (a) About how many microorganisms are found in the...Ch. 1 - Treat a cell in a human as a sphere of radius 1.0...Ch. 1 - An automobile tire is rated to last for 50 000...Ch. 1 - Bacteria and other prokaryotes are found deep...Ch. 1 - A point is located in a polar coordinate system by...Ch. 1 - A certain corner of a room is selected as the...Ch. 1 - Express the location of the fly in Problem 40 in...Ch. 1 - Two points in a rectangular coordinate system have...Ch. 1 - Two points are given in polar coordinates by (r, )...Ch. 1 - Given points (r1, 1) and (r2, 2) in polar...Ch. 1 - For the triangle shown in Figure P1.45, what are...Ch. 1 - A ladder 9.00 m long leans against the side of a...Ch. 1 - A high fountain of water is located at the center...Ch. 1 - A right triangle has a hypotenuse of length 3.00...Ch. 1 - In Figure P1.49, find (a) the side opposite , (b)...Ch. 1 - In a certain right triangle, the two sides that...Ch. 1 - In Problem 50, what is the tangent of the angle...Ch. 1 - Prob. 48PCh. 1 - A surveyor measures the distance across a straight...Ch. 1 - Prob. 50PCh. 1 - (a) One of lire fundamental laws of motion states...Ch. 1 - (a) Find a conversion factor to convert from miles...Ch. 1 - One cubic centimeter (10 cm3) of water has a mass...Ch. 1 - Prob. 54APCh. 1 - The displacement of an object moving under uniform...Ch. 1 - Assume it takes 7.00 minutes to fill a 30.0-gal...Ch. 1 - One gallon of paint (volume = 3.79 103 m3) covers...Ch. 1 - A sphere of radius r has surface area A = 4r2 and...Ch. 1 - Assume there are 100 million passenger can in the...Ch. 1 - Prob. 60APCh. 1 - (a) How many seconds are there in a year? (b) If...Ch. 1 - Imagine that you are the equipment manager of a...Ch. 1 - The nearest neutron star (a collated star made...
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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Similar questions
- A surveyor measures the distance across a straight river by the following method (Fig. P1.6). Starting directly across from a tree on the opposite bank, she walks d = 100 m along the riverbank to establish a baseline. Then she sights across to the tree. The angle from her baseline to the tree is 0 = 35.0. How wide is the river? Figure P1.6arrow_forwardOne student uses a meterstick to measure the thickness of a textbook and obtains 4.3 cm 0.1 cm. Other students measure the thickness with vernier calipers and obtain four different measurements: (a) 4.32 cm 0.01 cm. (b) 4.31 cm 0.01 cm, (c) 4.24 cm 0.01 cm, and (d) 4.43 cm 0.01 cm. Which of these four measurements, if any, agree with that obtained by the first student?arrow_forwardA surveyor measures the distance across a straight river by the following method: starting directly across from a tree on the opposite bank, he walks x = 1.00 102 m along the riverbank to establish a baseline. Then he sights across to the tree. The angle from his baseline lo the tree is = 35.0 (Fig. P1.53). How wide is the river? Figure P1.53arrow_forward
- In Figure P1.49, find (a) the side opposite , (b) the side adjacent to . (c) cos , (d) sin , and (c) tan . Figure P1.49arrow_forwardFigure P1.6 shows a frustum of a cone. Match each of the three expressions (a) (r1 + r2)[h2 + (r2 r1)2]1/2, (b) 2(r1 + r2), and (c) h(r12 + r1r2 + r22)/3 with the quantity it describes: (d) the total circumference of the flat circular faces, (e) the volume, or (f) the area of the curved surface. Figure P1.6arrow_forwardWhat is the x component of the vector shown in Figure OQ1.9? (a) 3 cm (b) 6 cm (c) 4cm (d) 6cm (e) none of those answers Figure OQ1.9 Objective Questions 9 and 10.arrow_forward
- A house is advertised as having 1 420 square feet under its roof. What is area in square meters? (a) 4 660 m2(b) 132 m2 (c) 158m2 (d) 132 m2 (e) 10.2m1arrow_forwardCalculate the result for each of the following cases using the correct number of significant figures. a. 3.07670 10.988 b. 1.0093 105 9.98 104 c. 5.44231064.008103arrow_forwardThe displacement vectors 42.0 cm at 15.0 and 23.0 cm at 65.0 both start from the origin and form two sides of a parallelogram. Both angles are measured counterclockwise from the x axis. (a) Find the area of the parallelogram. (b) Find the length of its longer diagonal.arrow_forward
- A sidewalk is to be constructed around a swimming pool that measures (10.0 0.1) m by (17.0 0.1) m. If the sidewalk is to measure (1.00 0.01) m wide by (9.0 0.1) cm thick, what volume of concrete is needed and what is the approximate uncertainty of this volume?arrow_forwardFigure 1.19 shows two vectors lying in the xy-plane. Determine the signs of the x- and y-components of A, B, and A+B.arrow_forwardUse the rules for significant figures to find the answer to the addition problem 21.4 + 15 + 17.17 + 4.003. (See Section 1.4).arrow_forward
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