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The acceleration vector for the spacecraft Dolphin 163 is given by a(t) =(-2 cos(t), 0,-2 sin(t)). It is also known that the velocity and position at t = 0 are (0) = (0, V5, 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 F(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. (d) At time t = seconds the spacecraft launches a probe in a direction opposite of N, the unit normal vector to r. 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?

The acceleration vector for the spacecraft Dolphin 163 is given by a(t) =(-2 cos(t), 0,-2 sin(t)). It is also known that the velocity and position at t = 0 are (0) = (0, V5, 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 F(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. (d) At time t = seconds the spacecraft launches a probe in a direction opposite of N, the unit normal vector to r. 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?

Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter3: Additional Topics In Trigonometry
Section3.3: Vectors In The Plane
Problem 11ECP
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The acceleration vector for the spacecraft Dolphin 163 is given by a(t) = (-2 cos(t), 0,-2 sin(t)). It is also known that the velocity and position att = 0 are (0) = (0, v5, 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 F(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. (d) At time t = A seconds the spacecraft launches a probe in a direction opposite of N, the unit normal vector to 7. 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?
Transcribed Image Text:The acceleration vector for the spacecraft Dolphin 163 is given by a(t) = (-2 cos(t), 0,-2 sin(t)). It is also known that the velocity and position att = 0 are (0) = (0, v5, 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 F(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. (d) At time t = A seconds the spacecraft launches a probe in a direction opposite of N, the unit normal vector to 7. 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?
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