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Clear Handwriting

1.

1. (3.5pts - show work, use g = 9.8m/s' and round your final answer to two decimal places as needed) A projectile is launched from the ground (thus, the initial position is (0, 0) ) with an initial speed of 150 m/s and angle to the horizontal of 60. (a) How long does it take for the projectile to hit the ground (b) Where does the projectile hits the ground and at what speed? (in other words, (a) find the time of flight, and (b) find the range and the speed, that is the magnitude of the velocity, at which the projectile hits the ground).2. (3.5pts , Show work; give exact answer) Find the unit tangent vector T, the principal unit normal vector N, and the unit binorrnal vector B for the helix r(t) : (cos :5, sin 13, t). 3. (3pts Show work; give exact answer) Consider the function f(:17,y) : may and the point P(2,0). (a) Find a unit vector that gives the direction of steepest ascent at P, and (b) Find a vector that points in a direction of no change in the function at P