question below:

A baseball is hit when it is 3 it above the ground. It leaves the bat with initial velocity of 197 ft/ sec at a launch angle of 13. At the instant the ball is hit, an instantaneous gust of wind blows against the ball, adding a component of - 19i (ft/sec) to the ball's initial velocity. A 10-ft-high fence lies 359 fl from home plate in the direction of the ight. The acceleration due to gravity is g = 32 ft/ secz. Complete parts (a) through (e). a. Find a vector equation for the path of the baseball. |'(t)=( )i+( it (Use integers or decimals for any numbers in the expression. Round to two decimal places as needed.) b. How high does the baseball go, and when does it reach its maximum height? The baseball reaches its maximum height of feet after seconds. (Round to two decimal places as needed.) c. Find the range and ight time of the baseball, assuming the ball is not caught. The range is feet, and the ight time is seconds. (Round to two decimal places as needed.) d. When is the baseball 9 ft high? How far (ground distance) is the baseball from home plate at that height? The baseball is 9 it high after seconds and seconds. (Round to two decimal places as needed. Use ascending order.) The baseball is feet or feet from home plate when it is 9 ft high. (Round to two decimal places as needed. Use ascending order.) 9. Has the batter hit a home run? Explain. O A. No because the ball hits the wall. 0 B. Yes because the ball goes over the wall. 0 C. No because the ball does not reach the wall. Find the curve's unit tangent vector. Also, find the length of the indicated portion of the curve. r(t) = (5cos t)i + (5sin t)j + (3t)k, Ostsx Find the curve's unit tangent vector. T(t) = The length of the curve is (Type an exact answer, using it as needed.)Find the curve's unit tangent vector. Also, nd the length of the indicated portion of the curve. 2 r(t)=8ti + []t3'2k, Osts 57 The curve's unit tangent vector is (Eh + 03)] + (D) k. (Type exact answers, using radicals as needed.) The length of the indicated portion of the curve is D units. (Type an integer or a simplied fraction.) Find the curve's unit tangent vector. Also, find the length of the indicated portion of the curve. r(t) = 10 cos 3+ j+ (10 sin t) k, Osts Find the curve's unit tangent vector. T(t) The length of the curve is (Type an exact answer, using it as needed.)