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8. [-/1 Points] DETAILS LARCALC11 12.4.052. Find the vectors T and N and the binormal vector B = T x N, for the vector-valued function r(t) at the given value of t. r(t) = 6 cos(2t)i + 6 sin(2t)j + tk, to = 4 T N 4 B Need Help? Read It Watch It 9. [-/1 Points] DETAILS LARCALC11 12.4.056. Use the vector-valued function r(t) to find the principal unit normal vector N(t) using the alternative formula (v . v)a - (v . a)v N = |(v . v)a - (v . a)vll' r(t) = 5 cos ti + 5 sin tj + 3tk N(t) =10. [-I1 Points] LARCALC11 12.4.057. ASK YOUR TEACHER Find the tangential and normal components of acceleration for a projectile fired at an angle 9 with the horizontal at an initial speed of V0 ft/s. T(f) = N(t) = What are the components when the projectile is at its maximum height? Need Help? 11. [-I1 Points] LARCALC11 12.4.068. ASK YOUR TEACHER An object of mass m moves at a constant speed V in a circular path of radius r. The force required to produce the centripetal component of acceleration is called the centripetal force and is given by F = mvzlr. Newton's Law of Universal Gravitation is given by F = GMm/dz, where dis the distance between the centers of the two bodies of masses M and m, and G is a gravitational constant. The speed required for circular motion is v = \\/ GM/r. Use the result above to find the speed necessary for the given circular orbit around Earth. Let GM = 9.56 x 104 cubic miles per second per second, and assume the radius of Earth is 4000 miles, (Round your answer to two decimal places The orbit of a communications satellite R miles above the surface of Earth that is in geosynchronous orbit. [The satellite completes one orbit per sidereal day (approximately 23 hours, 56 minutes), and therefore appears to remain stationary above a point on Earth.] mi/s 1. [-/1 Points] DETAILS LARCALC11 12.5.003. Sketch the plane curve. r(t) = 2ti - tj, [0, 2] N 4 N 1 1 X -1 2 3 4 5 -1 1 2 3 4 5 -1 -1 O -2 O -21 N 4 1 - 1 1 2 3 4 5 - 1 1 2 3 4 5 - 1 -1 O O -21 Find its length over the given interval.2. [-/1 Points] DETAILS LARCALC11 12.5.009. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHE The position of a baseball (in ft) is represented by r(t) = 55\\ 2ti + (3 + 55v2t - 16t2)j. Find the arc length of the trajectory (flight) of the baseball. (Let t = 0 represent when the ball is hit. Let j = 0 be ground level. Round your answ to one decimal place.) ft Need Help? Read It