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1. (20 points) The acceleration vector for the spacecraft Dolphin 163 is given by 6(t) = (2 cos(t), 0, 25in(t) ). It is also known that the velocity and position at t = 0 are 17(0) = (0, J5, 2) and F(0) = (3, 0,0 ). Assume distances are measured in kilometers (km) and time is measured in seconds (s). (a) Find the position function 7"(t) for the spacecraft. (b) Find the function for the speed of the spacecraft and the speed when t = 0. (c) Compute the curvature of the trajectory when t = 0. ((1) At time t = 7r seconds the spacecraft launches a probe in a direction opposite of N, the unit normal vector to F . If the probe travels along a straight line in the direction it was launched from the spacecraft for 5 km and then stops, what is its resting coordinate