MAT 111 Problem Set 2in Mathematics by lancer
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Instructions: Solve each of the following problems and show supporting work neatly. These are open book exercises and graphing calculators may be used.
The preferred procedure is to open this problem set in Microsoft Word and show your work beneath each problem using Mathtype to write the mathematical expressions. Submit the completed problem set assignment to your instructor by the end of Module 11 through the Assignment Tool. Using the word document is the preferred method of receiving your work. However, the work may be hand-written and scanned into a Word document, which can also be transmitted through the Assignment Tool located in Module 11.
(1) The escape velocity v a spacecraft needs to leave the gravitational field of a planet varies directly as the square root of the product of the planets radius R and its acceleration due to gravity g. For Mars and Earth:
Find for Mars if the escape velocity for earth,
(2) The distance s that an object falls due to gravity varies jointly as the acceleration g due to gravity and the square of the time t of fall. The acceleration due to gravity on the moon is 0.172 that on earth. If a rock falls for 2 seconds on earth, how many seconds would be required for the rock to fall an equal distance on the moon?
(3) On a test flight, during the landing of the space shuttle, the ship was 325 feet above the end of the landing strip. It then came in on a constant angle of 7.5 degrees with the landing strip. How far from the end of the landing strip did it first touch ground?
(4) The distance from the ground to the underside of a cloud is called the ceiling. A ground observer 950 m from a searchlight aimed vertically upward notes that the angle of elevation of the spot of light on a cloud is 76 degrees. What is the ceiling to the nearest meter?
(5) A jet is traveling westward with the sun directly overhead. That is, the jet is on a line between the sun and the center of the earth. How fast must the jet fly in order to keep the sun directly overhead? Assume that the earths radius is 3960 miles, the altitude of the jet is low, and the earth rotates about its axis once in 24 hours.
(6) A helicopter blade is 2.75 m long and is rotating at 420 rpm. What is the linear velocity of the tip of the blade?
(7) A plane travels at 120 mph in still air. It is headed due south in a wind of 30 mph from the northeast. What is the resultant velocity of the plane? Find the magnitude and the drift angle. The drift angle is the angle between the intended line of flight and the true line of flight.
(8) A rocket is launched with a vertical component of velocity of 2840 km/h and a horizontal component of velocity of 1520 km/h. What is the resultant velocity? Find both the magnitude and the direction.
(9) The velocity v of a rocket at the point at which its fuel is completely burned is given by the following equation. Solve for w.
(10) The velocity v of an object t seconds after it has been dropped from a height about the surface of the earth is given by the equation v = 32t feet per second, assuming no air resistance. If we assume that air resistance is proportional to the square of the velocity, then the velocity after t seconds is given by the following equation.
In how many seconds will the velocity be 50 feet per second?
Can an object reach a velocity of 100 feet per second? Show work to justify or explain your answer.