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Find the geodesics on a sphere. Hints: Use spherical coordinates with constant
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Mathematical Methods in the Physical Sciences
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- A projectile fired into the first quadrant from the origin of a coordinate system will pass through the point (x.y) at time t according to 2x the relationship cot 8= 2y + gt where e is the angle of elevation of the launcher and g is the acceleration due to gravity (32.2 feet/second?). An artilleryman is firing at an enemy bunker located 2700 feet up the side of a hill that is 6275 feet away. He fires a round, and exactly 2.89 seconds later he scores a direct hit. (a) What angle of elevation did he use? (Do not round until the final answer. Then round to one decimal place as needed ) (b) If the angle of elevation is also given by sec - E, where v, is the muzzle velocity of the weapon, find the muzzie velocity of the artillery piece he used. feet/second (Round to two decimal places as needed.) IIIarrow_forwardFind the curve's unit tangent vector. Also, find the length of the indicated portion of the curve. 4/2 312K r(t) = (2t cos t)i +(- 2t sin t)j + 3 The curve's unit tangent vector is ( Di+ ( + ( k. (Type exact answers, using radicals as needed.) Enter your answer in the edit fields and then click Check Answer.arrow_forwardFind the curve's unit tangent vector. Also, find the length of the indicated portion of the curve. 4/2 3/2k Ostsa 3 r(t) = (2t cos t)i + (2t sin t)j + The curve's unit tangent vector is (Oi+ (Di+ (O k. (Type exact answers, using radicals as needed.)arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage