(2000) Problem 4: A spaceship of mass 110 kg is going to use a planet for a grav
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(2000) Problem 4: A spaceship of mass 110 kg is going to use a planet for a gravitational assist-thatis, use the planet's gravity to change its direction of travel without expending any fuel. It is initially moving at a velocity of 270 m/s and at an angle of ?0 640, at a distance 11400 km from the center of the planet as shown in the figure 0 ©theexpertta.com × 50% Part (a) Give an expression for the angular momentum of the spacecraft, using the coordinate system specified, in terms of m, ro, vo PO. and unit vectors i. j, and k. Grade Summary 0% 100% Potential cos(a) cos(pcoS()( cos()sin(a) sin(po sin(e) Submissions Attempts remaining: 3 (0% per attempt) detailed view 7 89 HOME 096 096 END BACKSPACE DEL CLEAR Submit Hints: 2 for a 096 deduction. Hints remaining. Feedback: 0% deduction per feedback. 0 -Use the definition of angular momentum and the variables given in the problem. -Determine the radius vector (position vector) of the spaceship at a given instant. Find the component of velocity perpendicular to this position vector at given instant. Now find direction of angular momentum as direction of cross-product of position vector and velocity. -? 50% Part (b) If the spaceship whips around the planet to the other side so that the angle is ? = 42° and is moving at 140 m/s, how far, in kilometers, from the planet is it?Explanation / Answer
(A) L1 = m (r x v0)
L1 = m r v0 sin(phi0) ....Ans
(B) angular momentum will remain same.
L1 = L2
m r v0 sin(phi0) = m r2 v2 sin(phi)
(11400)(270)sin64 = r (140)sin42
r = 29532 km
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