7 Tutorial ExerciseThe parametric equations for the paths of two projectiles are given. At what rate is the distance between thetwo objects changing at the given value of t?X1= 13 cos(2t), Yı = 6 sin(2t)First objectX2 = 10 cos(t), Y2 = 4 sin(t)Second objectt = t/2Step 1Apply the distance formula to find the rate at which the distance is changing.V(x1- x2)2 + (Y1 – y2)?Distance =f(t) =Differentiate f(t) with respect to t.f(t) :(13 cos 2t – 10 cos t)2 + (6 sin 2t – 4 sin t)²-Vf '(t)(을)|(13 cos 2t -10 cos t)2 + (6 sin 2t –4 sin t)2[[o] + [)(-26 sin 2t + 10 sin(12 sin 2t8 sin t)(

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Tutorial Exercise The parametric equations for the paths of two projectiles are given. At what rate is the distance between the two objects changing at the given value of t? X1 = 13 cos(2t), yı = 6 sin(2t) First object X2 = 10 cos(t), Y2 = 4 sin(t) Second object t = r/2 Step 1 Apply dictanc banging

Tutorial Exercise The parametric equations for the paths of two projectiles are given. At what rate is the distance between the two objects changing at the given value of t? X1 = 13 cos(2t), yı = 6 sin(2t) First object X2 = 10 cos(t), Y2 = 4 sin(t) Second object t = r/2 Step 1 Apply dictanc banging

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter8: Polar Coordinates And Parametric Equations

Section8.FOM: Focus On Modeling: The Path Of A Projectile

Problem 7P: Shooting into the Wind Using the parametric equations you derived in Problem 6. draw graphs of the...

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Shooting into the Wind Suppose that a projectile is fired into a headwind that pushes it back so as to reduce its horizontal speed by a constant amount . Find parametric equations for the path of the projectile.
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Gear Trains Figure 8 shows a single-stage gear train. Gear trains are used in many products, such as clocks and automotive transmissions, to reduce or increase the angular velocity of a component. The size of each gear is measured by the number of teeth rather than the radius. Suppose the first gear has n1 and the second gear has n2 teeth. Because the spacing of the teeth is the same for both gears, the ratio of their radii will be equivalent to the corresponding ratio of the number of teeth. When two gears are meshed together, they share the same linear velocity. If 1 and 2 are the angular velocities of the first and second gears, respectively, then v2=v1r22=r112=r1r212=n1n21 The second gear in a single-stage gear train has 6 teeth and an angular velocity of 90 revolutions per minute. The first gear has 54 teeth. Find the angular velocity of the first gear.
Shooting into the Wind Using the parametric equations you derived in Problem 6. draw graphs of the path of a projectile with initial speed v0=32ft/s, fired into a headwind of =24ft/s, for the angles =5,15,30,40,45,55,60 and 75. Is it still true that the greatest range is attained when firing at 45 ? Draw some more graphs for different angles, and use these graphs to estimate the optimal firing angle.