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At time t= 0, a particle is located at the point (6,6,9). It travels in a straight line to the point (4,9,1), has speed 3 at (6,6,9) and constant acceleration - 2i + 3j- 8k. Find an equation for the position vector r(t) of the particle at time t. The equation for the position vector r(t) of the particle at time t is r(t) = + K. (Type exact answers, using radicals as needed.)1/4 Evaluate the integral [(1 + 3 cost) i + (3 sin t) j+ ( sect) k] at. - 1/4 The result is it K. (Type exact answers, using x and radicals as needed.)Solve the following initial value problem for r as a function of t. Differential equation: 2 = 2eti-e -tj + 12e 21 k dt Initial conditions: r(0) = 61 + 4j + 6k dr dt = - 2i + 5j It = 0 r(t)= + +A projectile is fired with an initial speed of 550 m/sec at an angle of elevation of 30". Answer parts (a) through (d) below.a. When will the projectile strike? sec (Round to one decimal place as needed.) b. How far away will the projectile strike? m (Round to the nearest meter as needed.) c. How high overhead will the projectile be when it is 5 km downrange? m (Round to the nearest meter as needed.) d. What is the greatest height reached by the projectile? m (Round to the nearest meter as needed.)A spring gun at ground level fires a golf ball at an angle of 45". The ball lands 10 m away. The acceleration due to gravity is g =9.8 m /s". What was the ball's initial speed? For the same initial speed, find the two firing angles that make the range 8 m. The initial speed of the ball is 9.90 m/sec. (Round to the nearest hundredth.) The two firing angles are degrees. (Round to the nearest tenth. Use a comma to separate answers as needed.)