Identify the velocity of an unidentified flying object (UFO) as it enters the and exit the Philippine Area of Responsibility. Calculate the resultant velocity. Use graphical and mathematical method. Express your answers in meters/second (m/s) and in correc number of significant figure. Scale for graphical method: 50 km/h :1 in Vector Velocity (m/s) Vx Vy 125 km/h SE 64 km/h 18° S of W 141 km/h 25° W of S
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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.)The plane carrying the supplies will be cruising at a constant velocity of 250 miles per hour relative to the ground and at a height of 2,650 meters above the target site. Using this information, create a supply drop plan including all required information and calculations outlined below. As you are completing your supply drop plan, remember that correct SI units are a required component of your calculations and descriptions. Using your understanding of kinematic equations and the given variables in the scenario, calculate the horizontal and vertical motion of the payload to ensure it arrives at the drop site. In your calculations, account for both the horizontal and vertical motion of the payload. Your calculations should address the following: A) Initial velocity of the payload when launched B) The velocity of the payload when it hits the groundThe 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
- a) A robin flies a distance of 45 963 cm. How far has it flown in kilometres?(b) What is the speed in metres per second of a car that is travelling at 82 km/h? (c) What is the speed in kilometres per hour of a 27.78 m/s baseball pitch?(d) How many seconds are there in a calendar year, given that a calendar year has 365.24 days in it? T/IKeiko drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 7 hours. When Keiko drove home, there was no traffic and the trip only took 5 hours. If her average rate was 18 miles per hour faster on the trip home, how far away does Keiko live from the mountains? Do not do any rounding.dV An oil tanker aground on a reef is forming a circular oil slick about 0.1 foot thick. To estimate the rate (in cubic feet per minute) at which the oil is leaking from the tanker, it was found that the radius of the slick was increasing at 0.31 foot dt dR dV per minute (- = 0.31) when the radius R was 400 feet. Find using T 3.14. dt dt Tanker A=TR? V=0.1A R dV ft3 /min dt (Type an integer or a decimal. Round to the nearest whole number as needed.)
- Supply all missing information with the correct numerical values. Do not include the units. Round off all answers to two decimal places. Do not forget the negative sign (-) if needed. Borsalino wants to buy some ice cream in the nearest convenience store. He has to walk 5.3 meters, 12 degrees in the north of east direction to reach the doorstep of the convenience store. He then enters the store and walks straight to cashier, two meters due northwest. Let A be the displacement vector with a magnitude of 5.3 meters directed 12 degrees in the north of east direction, and let B be the displacement vector with a magnitude of two meters due northwest. Express vectors A and B in unit vector component form. À = B = The net displacement is given by the vector sum: R = À +B. Ř= By Pythagorean theorem,the magnitude of the displacement is: meters. %3D The direction of the resultant displacement is: north of east.Supply all missing information with the correct numerical values. Do not include the units. Round off all answers to two decimal places. Do not forget the negative sign (-) if needed. Borsalino wants to buy some ice cream in the nearest convenience store. He has to walk 5.3 meters, 12 degrees in the north of east direction to reach the doorstep of the convenience store. He then enters the store and walks straight to cashier, two meters due northwest. Let Å be the displacement vector with a magnitude of 5.3 meters directed 12 degrees in the north of east direction, and let B be the displacement vector with a magnitude of two meters due northwest. Express vectors A and B in unit vector component form. A = B = + The net displacement is given by the vector sum: Ř =Á + B. + By Pythagorean theorem, the magnitude of the displacement is: |Ř = meters. The direction of the resultant displacement is: $ = north of eastSupply all missing information with the correct numerical values. Do not include the units. Round off all answers to two decimal places. Do not forget the negative sign (-) if needed. Borsalino wants to buy some ice cream in the nearest convenience store. He has to walk 5.3 meters, 12 degrees in the north of east direction to reach the doorstep of the convenience store. He then enters the store and walks straight to cashier, two meters due northwest. Let À be the displacement vector with a magnitude of 5.3 meters directed 12 degrees in the north of east direction, and let B be the displacement vector with a magnitude of two meters due northwest. Express vectors and in unit vector component form. %3! + B = + Ř=À +B. The net displacement is given by the vector sum: Ř= By Pythagorean theorem,the magnitude of the displacement is: IŘ = meters. !3! The direction of the resultant displacement is: north of east.
- Supply all missing information with the correct numerical values. Do not include the units. Round off all answers to two decimal places. Do not forget the negative sign (-) if needed. Borsalino wants to buy some ice cream in the nearest convenience store. He has to walk 5.3 meters, 12 degrees in the north of east direction to reach the doorstep of the convenience store. He then enters the store and walks straight to cashier, two meters due northwest. Let A be the displacement vector with a magnitude of 5.3 meters directed 12 degrees in the north of east direction, and let B be the displacement vector with a magnitude of two meters due northwest. Express vectors A and B in unit vector component form. A = B = î+ R = î. The net displacement is given by the vector sum: R=A+B. By Pythagorean theorem, the magnitude of the displacement is: IRI= meters. The direction of the resultant displacement is 4= north of east. 7Supply all missing information with the correct numerical values. Do not include the units. Round off all answers to two decimal places. Do not forget the negative sign (-) if needed. Borsalino wants to buy some ice cream in the nearest convenience store. He has to walk 5.3 meters, 12 degrees in the north of east direction to reach the doorstep of the convenience store. He then enters the store and walks straight to cashier, two meters due northwest. Let A be the displacement vector with a magnitude of 5.3 meters directed 12 degrees in the north of east direction, and let B be the displacement vector with a magnitude of two meters due northwest. Express vectors A and in unit vector component form. À= ぐー B = 7+ The net displacement is given by the vector sum: Ř =Á +B. Ř= 7+ By Pythagorean theorem,the magnitude of the displacement is: |Ř = meters. The direction of the resultant displacement is: 3D north of east.Supply all missing information with the correct numerical values. Do not include the units. Round off all answers to two decimal places. Do not forget the negative sign (-) if needed. Borsalino wants to buy some ice cream in the nearest convenience store. He has to walk 5.3 meters, 12 degrees in the north of east direction to reach the doorstep of the convenience store. He then enters the store and walks straight to cashier, two meters due northwest. Let A be the displacement vector with a magnitude of 5.3 meters directed 12 degrees in the north of east direction, and let B be the displacement vector with a magnitude of two meters due northwest. Express vectors A and B in unit vector component form. À = B - Î + The net displacement is given by the vector sum: R = Á + B. Ř = By Pythagorean theorem,the magnitude of the displacement is: |Ř| = meters. The direction of the resultant displacement is: north of east.