(a)
The distance at which a person will have to hold a European 2-euro coin to subtend an angle of
(a)
Answer to Problem 16Q
Solution:
1.49 m
Explanation of Solution
Given data:
A European 2-euro coin has a diameter of 2.6 cm. The angle subtended by the coin is
Formula used:
The small-angle formula is written as,
Here, α is the angle subtended by the object (in arcseconds), d is the distance between the observer and the object and D is the linear size of the object.
Explanation:
The distance at which a person will hold a 2-euro coin to subtend an angle of
Rearrange for d,
Since
Conclusion:
Hence, the coin should be held at 1.49 m if the angle to be subtended is
(b)
The distance at which a person will have to hold a European 2-euro coin to subtend an angle of
(b)
Answer to Problem 16Q
Solution:
89.3815 m
Explanation of Solution
Given data:
A European 2-euro coin has a diameter of 2.6 cm. The angle subtended by the coin is
Formula used:
The small-angle formula is written as,
Here, α is the angle subtended by the object (in arcseconds), d is the distance between the observer and the object and D is the linear size of the object.
Explanation:
The distance at which a person will hold a 2-euro coin to subtend an angle of
Rearrange for d,
Since
Conclusion:
Hence, the coin should be held at 89.4 m in order to subtend an angle of
(c)
The distance at which a person will have to hold a European 2-euro coin to subtend an angle of
(c)
Answer to Problem 16Q
Solution:
5362.9 m
Explanation of Solution
Given data:
A European 2-euro coin that has a diameter of 2.6 cm. The angle subtended by the coin is
Formula used:
The small-angle formula is written as,
Here, α is the angle subtended by the object (in arcseconds), d is the distance between the observer and the object and D is the linear size of the object.
Explanation:
The distance at which a person will hold a 2-euro coin to subtend an angle of
Rearrange for d,
Substitute 2.6 cm for D and
Conclusion:
Hence, the coin should be held at 5362.9 m in order to subtend an angle of
Want to see more full solutions like this?
Chapter 1 Solutions
Universe
- a method for determining the sizes of the orbits of pl from the sun than Earth. His method involved noting of days between the times that a planet was in the pc A and B in the diagram. Using this time and the num each planet's year, he calculated c and d. a. For Mars, c= 55.2 and d= 103.8. How far is Mars in astronomical units (AU)? One astronomical un the average distance from Earth to the center of th 93 million miles. b. For Jupiter, c 21.9 and d= 100.8. How far is Jup %3D sun in astronomical units? lo olpno er ort to rt .onte eteem-21 o to bre e ne ern 100 o ho aotem t elbl erl pnibioda lert pribiortarrow_forwardCalculate the angle a person needs to lean from the vertical when 1. walking a 14 m (radius) circular track at 22 mins per mile, and Enter to 2 significant figures Angle with respect to the vertical = = 0.85 ! No, that's not the correct answer. O 2. running at 4 min per mile. Enter to 2 significant figures Angle with respect to the vertical = 6.8 Use 1 mile = 1609.4 m Sense-making: Do your results for the leaning angle during walking agree with your observations about people walking on circular tracks? Oarrow_forwardIf you start at the equator and travel to 10 degrees north approx. how many kilometers (or miles) north of the equator will you be? Take the circumference of earth to be 40,000 kilometers (24,900) miles).arrow_forward
- If city is located in 2.8° north latitude and 46.0° east longitude. From there, you want to fly to a city in 7° north latitude and 52° east longitude. How much is the arc length of the big circle at 11000 m when the earth's radius is 6370 km? The arc length is 14223 km. Give your answer rounded to one kilmetre. Your last answer was interpreted as follows: 14223 XAnswer is incorrect. Keep centre of Earth as origin and define vectors to cities. Try again.arrow_forwardI measured the angular separation of Jupiter's moons in arcminutes/arcseconds and converted this angle to radians. The conversion factor for degrees to radians was 57.3 degrees per radian. Which unit of measurement is larger? 1 degree or 1 radian?arrow_forward(the complete question is in the picture) If the Newtonian constant has units G = [N · m2/kg2], the speed of light has units c = [m/s], the mass has units M = [kg] and the SI unit newtons is equivalentto N = [kg · m/s2], what are the units of the relation GM/c3?A. [kg · s]B. [kg · m2/s]C. [m2/s]D. [s]arrow_forward
- Oxygen Atoms in People. Figure 5.7 shows that oxygen makes up about 65% of the mass of a human being. A single oxygen atom has a mass of 2.66 × 10−26 kg. (a) Use this fact to estimate the number of oxygen atoms in your body. (Hint: If you know your weight in pounds, you can convert to kilograms by dividing by 2.2.) (b) Compare your answer to the number of stars in the observable universe (which is roughly 1022).arrow_forwardA small light source located 1 mm in front of a 1-m2m2 opening illuminates a wall behind. If the wall is 1 mm behind the opening (2 mm from the light source), the illuminated area covers 4 m2m2. How many square meters are illuminated if the wall is 3 mm from the light source? 5 mm? 10 mm?arrow_forwardI'm having trouble completing the problem I've attached a picture of below. I was able to find the the Earth's average speed in m/s relative to the sun by doing (2pi*(1.49x10^11))/31536000. But I am struggling to find the average velocity for the same thing over a period of one year in m/s. I was wondering how to calculate that? I've tried doing the (final velocity-initial velocity)/2 but the program doesn't accept my answer when using that approach.arrow_forward
- Stars are spherical in shape. A star has a diameter of 77 x 1010 m. How many earths could fit inside this star. Diameter of earth 12800 km Note: Write the answer in scientific representation after rounding to two decimal places. Answer:arrow_forwardUsing a single dimensional equation, estimate the number of steps it would take a person with a step length of 2.65 ft to walk from the Earth to Alpha Centauri a distance of 4.37 light-years. The speed of light is 1.86282 x 105 miles/s. Number of Steps = Enter your answer in accordance to the question statement x 1017arrow_forwardA planet's speed in orbit is given by V = (30 km/s)[(2/r)-(1/a)]0.5 where V is the planet's velocity, r is the distance in AU's from the Sun at that instant, and a is the semimajor axis of its orbit. Calculate the Earth's velocity in its orbit (assume it is circular): What is the velocity of Mars at a distance of 1.41 AU from the Sun? What is the spacecraft's velocity when it is 1 AU from the Sun (after launch from the Earth)? What additional velocity does the launch burn have to give to the spacecraft? (i.e. What is the difference between the Earth's velocity and the velocity the spacecraft needs to have?) How fast will the spacecraft be traveling when it reaches Mars? Does the spacecraft need to gain or lose velocity to go into the same orbit as Mars?arrow_forward
- Horizons: Exploring the Universe (MindTap Course ...PhysicsISBN:9781305960961Author:Michael A. Seeds, Dana BackmanPublisher:Cengage LearningAn Introduction to Physical SciencePhysicsISBN:9781305079137Author:James Shipman, Jerry D. Wilson, Charles A. Higgins, Omar TorresPublisher:Cengage LearningAstronomyPhysicsISBN:9781938168284Author:Andrew Fraknoi; David Morrison; Sidney C. WolffPublisher:OpenStax
- Stars and Galaxies (MindTap Course List)PhysicsISBN:9781337399944Author:Michael A. SeedsPublisher:Cengage Learning