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- Suppose [V]=L3,[]=ML3, and [t]=T . (a) What is the dimension of dV? (b) What is the dimension of dV/dt? (c) What is the dimension of (dV/dt)?A surveyor measures the distance across a river that flows straight north by the following method. Starting directly across from a tree on the opposite bank, the surveyor walks 100 m along the river to establish a baseline. She then sights across to the tree and reads that the angle from the baseline to the tree is 35 . How wide is the river?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.)
- (a) Estimate the density of the Moon. (b) Estimate the diameter of the Moon. (c) Given that the Moon subtends at an angle of about half a degree in the sky, estimate its distance from Earth.In (Eigure 1), a = 4 in, b=9 in, c= 7 in. Figure 1 of 1 Part A Locate the centroid of the area. Express your answer to three significant figures and include the appropriate units. Value Submit HÅ Provide Feedback Request Answer Units ?B. Find the slope of the curve at the given pol 11. y=4-3x² at (-1, 1) 12 y=x²-5 at (1, - 4)
- A&B are correct , just need help with C. Asap plzz,,Need help with a) and b). second picture is the answer for b)Please use the origin (0,0) as the starting point of the graph and 2pi on the x-axis as the point where th graph ends. Find a function of the form y = Asin(x) or y = Acos(x) whose graph matches the function below. 51 37/2 -2 -3 -4 -5+ Give an exact answer using fractions and/or multiples of pi as necessary. y = OType here to search
- Draw FBDs, determine '+' directions, redraw if necessary, write ΣF equations, set equal to 0 or ma, solve, box, and unitize. Find T1 and T2.Find the y coordinate of the centroid of the region shaded in the following diagram. 9 in. -27 in.Pls help ASAP. Pls show all work and explain thoroughly on what equation is being used and how you come up with the answer. Also, pls underline or square the final answers.