MATH 149 Spring 2007 Recitation 3 Problems Wednesday 21 March 2007 1 A poster of 500 square inches is to have a margin of 6 inches at the top and 4 inches at each side and the bottom What dimensions yield the largest printed area 2 An athletic field with a 400 perimeter consists of a rectangle with a semicircle at each end Find the dimensions of the field so that the area of the rectangular portion is the largest possible 3 Find the tangent line to the curve y D 4 x 2 at a point in the first quadrant that cuts from the first quadrant a triangle of minimum area 4 Describe the isosceles triangle of maximum area if two sides have a fixed length s 5 An object with weight W is dragged along a horizontal plane by a force acting along a rope attached to the object If the rope makes an angle with the plane then the magnitude of the force is FD W sin C cos where is a positive constant called the coefficient of friction and where 0 2 Show that F is minimized when tan D 6 The frame for a kite is to be made from six pieces of wood The four exterior pieces have been cut with the lengths indicated in the figure two of length a and two of length b To maximize the area of the kite how long should the diagonal pieces be See figure of kite on page 285 in Stewart 7 A boat leaves a dock at 2 00 P M and travels due south at a speed of 20 km h Another boat has been heading due east at 15 km h and reaches the same dock at 3 00 P M At what time were the two boats closest together 8 Show that for motion in a straight line with constant acceleration a initial velocity v 0 and initial displacement s0 the displacement after time t is 1 s D at 2 C v0 t C s0 2 9 An automobile is traveling on a straight road at 88 feet per second 60 mph What constant negative acceleration is required to stop the car in 40 feet 10 A model rocket is fired vertically upward from rest Its acceleration for the first three seconds is a t D 60t at which time the fuel is exhausted and it becomes a freely falling body Fourteen seconds later the rocket s parachute opens and the downward velocity slows linearly to 18 ft s in 5 s The rocket then floats to the ground at that rate a Determine the position function s and the velocity function v for all times t Sketch the graphs of s and v b At what time does the rocket reach its maximum height and what is that height c At what time does the rocket land 1 MATH 149 Spring 2007 Recitation 3 Problems Wednesday 21 March 2007 11 A canister is dropped from a helicopter 500 meters above the ground Its parachute does not open but the canister has been designed to withstand an impact velocity of 100 meters per second Will it burst 12 In an automobile race along a straight road car A passed car B twice Prove that at some time during the race their accelerations were equal State the assumptions that you make AMS LATEX 2
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