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- The first atomic bomb was detonated on July 16, 1945, at the Trinity test site about 200 mi south of Los Alamos. In 1947, the U.S. government declassified a film reel of the explosion. From this film reel, British physicist G.I. Taylor was able to determine the rate at which the radius of the fireball from the blast grew. Using dimensional analysis, he was then able to deduce the amount of energy released in the explosion, which was a closely guarded secret at the time. Because of this, Taylor did not publish his results until 1950. This problem challenges you to recreate this famous calculation. (a) Using keen physical insight developed from years of experience, Taylor decided the radius rof the fireball should depend only on time since the explosion, t, the density of the air, , and the energy of the initial explosion, E. Thus, he made the educated guess that r=kEabtcfor some dimensionless constant kand some unknown exponents a,b, and c. Given that [E]=ML2T-2 , determine the values of the exponents necessary to make this equation dimensionally consistent. (Hint: Notice the equation implies that k=rEabtcand that [k]=1 ). (b) By analyzing data from high-energy conventional explosives, Taylor found the formula he derived seemed to be valid as long as the constant khad the value 1.03. From the film reel, he was able to determine many values of rand the corresponding values of t. For example, he found that after 25.0 ms, the fireball had a radius of 130.0 m. Use these values, along with an average air density of 1.25kg/m3 , to calculate the initial energy release of the Trinity detonation in joules (J). (Hint: To get energy in joules, you need to make sure all the numbers you substitute in are expressed in terms of SI base units.) (c) The energy released in large explosions is often cited in units of “tons of TNT” (abbreviated “t TNT”), where 1 t TNT is about 4.2 GJ. Convert yow answer to (b) into kilotons of TNT (that is, kt TNT). Compare your answer with the quick-and-duty estimate of 10 kt TNT made by physicist Enrico Fermi shortly after witnessing the explosion from what was thought to be a safe distance. (Reportedly, Fermi made his estimate by dropping some shredded bits of paper right before the remnants of the shock wave hit him and looked to see how far they were carried by it.)46. Given the equation F- m/R, what relationship exists between each of the following? (1.3) a. Fand R b. Fand m c. Fand vThe height of a certain hill (in feet) is given by h(x, y) = 10 (2xy - 3 x^2 - 4y^2 -18x +28y + 12), where y isthe distance in miles (north), x the distance east of South Hadley, Massachusetts.a.) Where is the top of the hill located? b.) How high is the hill? c.)How steep is the slope (in feet per mile) at a point 1 mile north and one mile east of South Hadley? Inwhat direction is the slope steepest, at that point? d.) Make a contour map and a 3D plot of the area surrounding South Hadley, from 8 miles west to 4 mileseast, and 2 miles south to 8 miles north. Plot only positive heights on the 3D graph; use If to help youout
- What is the greatest distance on the surface of the earththat can be seen from the top of Mayon volcano whichis 2.4 kilometers high if the radius of the earth is 6370 km? (Illustrate and use trigonometric functions and identities) A. 159.7 km B. 174.8 kmC. 179.7 km D. 189.7 kmi need help on this hw question. final answers should include correct significant digit/decimal places/units. thank you.Solve the problem. The angle of elevation 0 of the sun in the sky at any latitude Lis calculated with the formula sine-cos D cos L cos o sanD sin L wis the number of radians that the Earth has rotated through since noon when w-0. Dis the declination of the sun. Westville has latitude L-379. Find the angle of elevation 0 in degrees of the sun at 3 PM on February 29, 2012, where at that time D-01e5 and w0.7854 368 O 28 26.9
- Pls. answer correctly and provide complete solution. Thank you.Revie A = 252 - 12ý, and B = 2.02 + 15. Express A- Bin unit vector notation. Express your answer using two significant figures. Express your answer in terms of the unit vectors and y. V AE Submit Reguest Answer Part B Express B-A in unit vector notation. Express your answer using two significant figures. Express your answer in terms of the unit vectors a and y. VO AEd B-A= PearsonD only !! I have A-C A. 24750 B. -47250 C.-22500 D. ??? I got 0.0675 but it's wrong help!
- Unginal number. A.) 149,600,000 B. 0.000000028 2 Move the decimal point to the right or the left to make the number between 1 and 10. Count the number of decimal places moved and note the direction. A. 1.49600000 = 8 places to the left B. 00000002.8 = 8 places to the right 3Rewrite the number deleting all extra zeros to the right or to the left of the decimal point.A cylindrical rod is 6.21 m long and has a diameter of 1.77 in. Calculate its volume, V, in cubic meters. Useful fact: 1 in. = 25.4 mm. If the volume is V = nx10m. enter the number n below. Do not give us the volume V. Give your answer correct to two decimnal places. n3D Typeyour answer.econds squared, Ol 72. n divide out and T = VT². The factor 2T has no units so a in the analysis. 10. The period of rotation of the Sun is 2.125 x 10° seconds. This is equivalent to 2.125 (3) Ms (1) us (2) ms (4) Ts 11. Human hair grows at the rate of 3 nanometers per second. This rate is equivalent to (1) 3 x 10-3 m/s (2) 3 x 10-6 m/s (3) 3 x 10-9 m/s (4) 3 x 10-12 m/s 12. The wavelength of red light is 7 x 10-7 meter. Express this value in nanometers. 13. If m represents mass in kg, v represents speed in m/s, and r represents radius in m, show that the force F in the formula F = in the unit kg m/s?. mv? can be expressed 14. If PE, represents the potential energy stored in a spring in kg m2/s², and x represents the change in spring length from its equilibrium position in m, what is the unit for the spring constant k in the formula PE, = }kx?
