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- A marathon runner completes a 42.188-km course in 2 h, 30 min, and 12s. There is an uncertainty of 25 m in the distance traveled and an uncertainty of 1 s in the elapsed time. (a) Calculate the percent uncertainty in the distance. (b) Calculate the percent uncertainty in the elapsed time. (C) What is the average speed in meters per second? (d) What is the uncertainty in the average speed?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.)What is wrong with the following expressions? How can you correct them? (a) C=AB , (b) C=AB , (c) C=AB , (d) C=AB , (e) C+2A=B , (f) C=AB , (g) AB=AB , (h) C=2AB , (i) C=A/B , and (j) C=A/B .
- 1%A9 li. t LTET 4G+ Vol) O A X O U 9:-7 Second H.W.pdf 1. Draw and label the vector with these components. Then determine the magnitude and angle of the vector. a- Az = 3 ,A, = -2 b- B, = -2 ,B, = 2 2. What is the speed of horse in meter per second that runs a distance of 1.2 miles in 2.4 minutes? 3. A car moving along X- axis according on the function: X (t) = 2 t2 + 5t +7 on [1,2] Find: a- The average velocity. b- The acceleration at 3s. 4. Julie is walking around a track at a 2m/s for some exercise. She then decides to start jogging so she accelerates at a rate of 0.5m/s? for 3 seconds. How far did Julie travel from the time she started to accelerate to the end of the 3 seconds? 5. Ralph uses a 2000 to do this. force to push his car along a road for 1000 m. It takes him500 s a- Calculate the amount of work that Ralph did on the car. b- Calculate the amount of power that he generated. IIPo = 25 uc/m³ is distributed uniformly through a certain region. If V=50 at y = 2 and V= 90 at y = 5, &, = 2. a- Give the solution and calculate V, E. b- Draw V, Ē, IE with respect to y-axis. c- Now if p₂ = 0, give the solution and calculate V, Ē.A0.8 (Homework) For the graph of vx versus t shown, estimate the following: i) What is the slope of the tangent line at t = 0.6 ? ii) What is the slope of the tangent line at t = 1.0 ? iii) What is the slope of the tangent line at t = 1.4 ? 2 -1-
- The continuity equation satisfied by u = 4xy+y?, v= 6xy+ 3y 10 u= 3x^2-2y^2, v=-6xy .II O u=x-4y, v=y-4x .IIIOI need the answer in number 7 with complete solution and units based on the given problem. Also do not round off and only round off in the final answer in 3 decimal placesPlease help me solve the following. Just the table and number 6.
