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Guest
Guest
1. Your team is on a space shuttle and you decide to dock at a nearby space station to refuel. As you approach the space station, you pick up transmissions from three beacons which mark the corners of the triangular landing zone on the space station. These transmissions are
beacon 1 = .61i + 2.00j + 2.76k
beacon 2 = .47i + 4.00j + 4.45k
beacon 3 = .47i + 2.00j + 4.45k
Write a function D(Xo,Yo,Zo) which takes your present position (Xo,Yo,Zo) as input and gives your distance from the closest point on the plane of the landing zone. Describe how you got this function. Include units.
2. What distance does your function give you at the instant the shuttle passes through the point 2.9i +4.00j +4.22k?
3. Your space shuttle is coasting with velocity vector V = -.25i + .34j +2.45k (units per minute.) Write a vector expression P(t) of your line of travel, parameterized by time, where t=0 corresponds to the point in part 2.
4. Assume that the space station is not moving and that you want to land in the landing zone. But you will miss if you stay on your present course. You have enough fuel aboard for one short blast which could propel a resting shuttle in any direction with velocity vector of magnitude at most 5.14 Units/min. Find a propulsion velocity vector p such that if you fire your rockets with this vector at time t=0, then your approach velocity vector (the combination of your propulsion velocity vector and your coasting velocity vector) will enable you to land somewhere within the landing zone. Be sure to show that vector p does not exceed the capacity of your engines and that you will actually hit within the landing zone.
5. Assuming you do what you set out to do in part 4, exactly when and where will you hit the landing zone?
6. You will hit the landing zone along an approach vector. Find the component of this approach vector that is perpendicular to the landing zone. Your shuttle can only survive an impact with a perpendicular impact of less than .284 units/minute. Will your shuttle survive the impact? Justify your answer. If you will crash, go back and redo your choice of vector p within the necessary parameters until you can avoid a crash.
beacon 1 = .61i + 2.00j + 2.76k
beacon 2 = .47i + 4.00j + 4.45k
beacon 3 = .47i + 2.00j + 4.45k
Write a function D(Xo,Yo,Zo) which takes your present position (Xo,Yo,Zo) as input and gives your distance from the closest point on the plane of the landing zone. Describe how you got this function. Include units.
2. What distance does your function give you at the instant the shuttle passes through the point 2.9i +4.00j +4.22k?
3. Your space shuttle is coasting with velocity vector V = -.25i + .34j +2.45k (units per minute.) Write a vector expression P(t) of your line of travel, parameterized by time, where t=0 corresponds to the point in part 2.
4. Assume that the space station is not moving and that you want to land in the landing zone. But you will miss if you stay on your present course. You have enough fuel aboard for one short blast which could propel a resting shuttle in any direction with velocity vector of magnitude at most 5.14 Units/min. Find a propulsion velocity vector p such that if you fire your rockets with this vector at time t=0, then your approach velocity vector (the combination of your propulsion velocity vector and your coasting velocity vector) will enable you to land somewhere within the landing zone. Be sure to show that vector p does not exceed the capacity of your engines and that you will actually hit within the landing zone.
5. Assuming you do what you set out to do in part 4, exactly when and where will you hit the landing zone?
6. You will hit the landing zone along an approach vector. Find the component of this approach vector that is perpendicular to the landing zone. Your shuttle can only survive an impact with a perpendicular impact of less than .284 units/minute. Will your shuttle survive the impact? Justify your answer. If you will crash, go back and redo your choice of vector p within the necessary parameters until you can avoid a crash.